HSND-2015, IPR. Department of Physics, University of Burdwan, Burdwan, West Bengal.

Size: px
Start display at page:

Download "HSND-2015, IPR. Department of Physics, University of Burdwan, Burdwan, West Bengal."

Transcription

1 New kind of deaths: Oscillation Death and Chimera Death HSND-2015, IPR Dr. Tanmoy Banerjee Department of Physics, University of Burdwan, Burdwan, West Bengal.

2 Points to be discussed Oscillation suppression Amplitude death (AD) Oscillation death (OD) Nontrivial AD (newly discovered) AD-OD Transition: First Experimental evidence AD-NAD Transition (newly discovered) Chimera death Conclusion

3 Collective behavior Natural systems are rarely isolated Coupled Oscillators provide a useful paradigm for the study of collective behavior of large complex systems Coupled oscillators show a plethora of complex collective behaviors such as: Synchronization Phase-locking Oscillation quenching Weak coupling: phase effect Strong coupling: Amplitude effect Newton s law of motion

4 Amplitude Death (AD) Amplitude death (AD) is one of the intriguing phenomena that occurs in coupled oscillators when they interact in such a way as to suppress each others oscillations and collectively go to the stable fixed point that was unstable otherwise. In many practical situations AD is desirable, as for example in laser applications and neuronal activity where a constant output is needed and fluctuations should be suppressed. Bar-Eli who showed that two interacting model continuous stirred tank reactors can stop oscillations and arrive at steady states if coupled diffusively. Bar Eli effect

5 Consider two diffusively coupled Stuart-Landau oscillators Earlier studies of coupled Landau-Stuart oscillators by Aronson et al. have shown that amplitude death is only possible for instantaneous coupling when the intrinsic frequencies are disparate Thus to achieve AD parameter mismatch is essential in the instantaneous coupling.

6 Time-delay coupling: AD is possible in identical oscillators Pioneering work group of Prof. Sen [Reddy et al, PRL]. showed that with time delay, death occurs even for identical oscillators with Time delay is ubiquitous in real systems due to finite propagation speed of signals, finite reaction times of Chemical reactions, finite response time of synapses, etc.

7 Geometrical interpretation The current state P(t) is pulled towards the retarded state Q(t-τ) of the other oscillator and vice-versa. For appropriate values of K and time delay both oscillations will spiral inwards and die out. (Reddy, Sen and Johnston, Phys. Rev. Letts. 80 (1998) 5109; Physica D 129 (1999) 15 )

8 Experimental verification carried out on coupled nonlinear oscillators (Reddy, Sen, Johnston, PRL, 85 (2000) 3381)

9 Instantaneous coupling ALSO can induce AD in identical oscillator Conjugate coupling Dynamic coupling Mean-field coupling Mean-field coupling is one of the most widely studied topics because of its presence in many natural phenomena in the field of biology, physics, and engineering. In the genetic oscillators interacting through a quorum-sensing mechanism, the occurrence of OD is shown where the concentration of the autoinducer molecule that can diffuse through the cell membrane contains a mean-field term. In three dimensional Ising spin model the mean-field interaction explains ferromagnetism.

10 Amplitude Death Vs. Oscillation Death

11 There are two distinct types of oscillation quenching processes: amplitude death (AD) and oscillation death (OD). In AD coupled oscillators arrive at a common stable steady state which was unstable otherwise and thus form a stable homogeneous steady state (HSS). But, in the case of OD, oscillators populate different coupling dependent steady states and thus gives rise to stable inhomogeneous steady states (IHSS); in the phase space OD may coexist with limit cycle oscillations.

12 AD is important in the case of control applications where suppression of unwanted oscillations is necessary e.g., in Laser application, neuronal systems, etc. On the other hand, OD is a much more complex phenomenon because it induces inhomogeneity in a rather homogeneous system of oscillators that has strong connections and importance in the field of biology (e.g., synthetic genetic oscillator, cellular differentiation), physics, etc.

13 Although, AD and OD are two structurally different phenomena--their genesis and manifestations are different, but for many years they are (erroneously) treated in the same footing. Only recently pioneering works by Koseska et al established the much needed distinctions between AD and OD. Although an extensive research work has been reported on AD, but the phenomenon of OD is a less explored topic.

14 Koseska et al show: AD and OD can simultaneously occur in diffusively coupled Stuart-Landau oscillators. An important transition phenomenon, namely the transition between AD to OD in Stuart-Landau oscillators with parameter mismatch. They established that the transition occurs due to the interplay between the heterogeneity and the coupling parameter that is analogous with the Turing type bifurcation in spatially extended systems. The group of Dr. Shyamal Dana shows the transition between AD and OD in identical nonlinear oscillators that are coupled diffusively and perturbed by a symmetry breaking repulsive coupling link.

15 In the previous studies... It was believed that the mean-field coupling in oscillators can induce AD only For the first time we show that Mean-field coupling can induce OD and AD-OD transition even in identical oscillators.

16

17 We consider N Stuart-Landau oscillators interacting through mean-field diffusive coupling Equilibrium points

18 Eigenvalues of the trivial fixed point Two pitchfork bifurcations Two Hopf bifurcations

19 Bifurcation diagram using XPPAUT

20 A NEW AD state! NTAD state is unique in comparison with its conventional counterpart in, at least, two way: First, unlike AD that has two possible routes: Hopf and saddle-node bifurcation, the NTAD state is born via a subcritical pitchfork bifurcation. Second, in sharp contrast with the AD, which is supported or enhanced by parameter mismatch, the NT-AD state is completely destroyed by parameter mismatch. In the NT-AD state we have two different solutions: x1=x2, and -x1=-x2; occurrence of one of this two states is determined by the initial conditions. This initial condition dependent amplitude death state is not observed earlier.

21

22

23 Effect of parameter mismatch NTAD vanishes for ANY parameter mismatch

24 256 Stuart- Landau oscillators

25 The FIRST experimental observation of the AD to OD transition T. Banerjee and D. Ghosh, Experimental observation of a transition from amplitude to oscillation death in coupled oscillators, Phys. Rev. E, 89, 2014.

26 Although OD and AD have been separately observed previously in a number of different dynamical systems, to the best of our knowledge, hitherto no experimental confirmation of the predicted AD-OD transition has been reported. We report the first experimental evidence of AD-OD transition in coupled oscillators. For this we consider two Van der Pol oscillators in their stable oscillation mode coupled via mean-field diffusion.

27 a=0.35

28

29 AD OD For Q<Q*, AD to OD transition occurs Experimental OD For Q>Q* no AD, thus only limit cycle to OD Experimental

30 Theoretical and experimental results: close matching in parameter space

31 Direct-Indirect Coupling Induced AD, OD and NAD D. Ghosh and Tanmoy Banerjee (2014) "Transitions among the diverse oscillation quenching states induced by the interplay of direct and indirect coupling", Physical Review E, 90(6), DOI: /PhysRevE (arxiv preprint: [nlin.cd], 2014).

32 This coupling scheme was introduced by Resmi et al. [Phys. Rev. E, 84, (2011)] as a general scheme to induce amplitude death (AD) in nonlinear oscillators. We show that apart from AD, it can induce OD and a new AD state, namely NAD state and the following transitions: AD-OD transition AD-NAD transition This NAD state has not only a nonzero homogeneous steady state but, more significantly, in this state the system becomes bi-stable

33 Stuart-Landau oscillator Environmental or indirect coupling Diffusive or direct coupling

34

35 d=1.5

36 AD-OD AD-NAD

37 More fine structures

38 Experimental set up

39 Experimental observation

40 Chimera death Tanmoy Banerjee (2014) "Chimera death induced by the mean-field diffusive coupling", arxiv preprint: arxiv: [nlin.cd], 2014.

41 Recently a novel dynamical state, called the chimera death, is discovered in a network of non locally coupled identical oscillators [A. Zakharova, M. Kapeller, and E. Sch\"{o}ll, Phy.Rev.Lett. 112, (2014)], which is defined as the coexistence of spatially coherent and incoherent oscillation death state. This state arises due to the interplay of non locality and symmetry breaking and thus bridges the gap between two important dynamical states, namely the chimera and oscillation death. The chimera is an intriguing spatio-temporal dynamical state where the synchronous and asynchronous behavior are observed simultaneously in a network of coupled identical oscillators. After its discovery in phase oscillators the chimera state attracts immediate attention due to its surprisingly complex behavior and a possible connection with many real world phenomena such as unihemispheric sleep in certain species, the multiple time scales of sleep dynamics, etc.

42 Although both chimera and oscillation death state induce inhomogeneity in a rather homogeneous network of oscillators, but their inter connection was not identified until the recent pioneering work by Zakharova et al. The authors reported an important discovery of a new state, which they called the chimera death, and established the much speculated connection between the chimera and oscillation death. According to Zakharova et al, chimera death (CD) is the steady state version of chimera, i.e., the population of oscillators in a network splits into incongruous coexisting domains of spatially coherent OD (where neighboring nodes attain essentially the same branch of the inhomogeneous steady state) and spatially incoherent OD (where the neighboring nodes jump among the different branches of inhomogeneous steady state in a completely random sequence).

43 For the first time, we show that a nonlocal coupling is not an essential ingredient to achieve Chimera death.

44 IPS Global AD CIMERA DEATH

45 Multi-cluster Chimera death

46 It is noteworthy that the choice of initial condition is crucial for obtaining chimera but still it is not well understood (see, e.g., Ref.\cite{raj} where it is commented ``the role of initial conditions in the emergence of chimera states and the existence of multistability needs to be explored in the future"). We believe that this study will initiate the search for the chimera death in other coupling schemes that are not non local in topology and at the same time open up the research to engineer multi-cluster chimera death state in electronic and biological networks.

47 Conclusion OD is a new state in comparison with AD New kind of oscillation suppression states (NAD, Chimera death, etc.) await further exploration Studies on OD is still in its infancy and need further studies Continuation software package like XPPAUT is indispensible to study OD

48 Acknowledgements Prof. B. C. Sarkar (University of Burdwan) Research scholars: Mr. Debabrata Biswas Mrs. Debarati Ghosh Mr. Bishwajit Paul Mr. Biswajit Karmakar SERB (DST) for providing FAST TRACK RESEARCH PROJECT for young scientists

49 Thank you

DR. TANMOY BANERJEE. Contact Information

DR. TANMOY BANERJEE. Contact Information DR. TANMOY BANERJEE Assistant Professor Department of Physics University of Burdwan Burdwan 713104 West Bengal India Email: tbanerjee@phys.buruniv.ac.in, tanbanrs@yahoo.co.in URL: http://www.researchgate.net/profile/tanmoy_banerjee

More information

Synchronization in delaycoupled bipartite networks

Synchronization in delaycoupled bipartite networks Synchronization in delaycoupled bipartite networks Ram Ramaswamy School of Physical Sciences Jawaharlal Nehru University, New Delhi February 20, 2015 Outline Ø Bipartite networks and delay-coupled phase

More information

= F ( x; µ) (1) where x is a 2-dimensional vector, µ is a parameter, and F :

= F ( x; µ) (1) where x is a 2-dimensional vector, µ is a parameter, and F : 1 Bifurcations Richard Bertram Department of Mathematics and Programs in Neuroscience and Molecular Biophysics Florida State University Tallahassee, Florida 32306 A bifurcation is a qualitative change

More information

Revival of oscillation from mean-field induced death: Theory and experiment

Revival of oscillation from mean-field induced death: Theory and experiment Revival of oscillation from mean-field induced death: Theory and experiment Debarati Ghosh 1, Tanmoy Banerjee 1, and Jürgen Kurths,3,4,5 1 Department of Physics, University of Burdwan, Burdwan 713 104,

More information

Dynamical Systems and Chaos Part II: Biology Applications. Lecture 10: Coupled Systems. Ilya Potapov Mathematics Department, TUT Room TD325

Dynamical Systems and Chaos Part II: Biology Applications. Lecture 10: Coupled Systems. Ilya Potapov Mathematics Department, TUT Room TD325 Dynamical Systems and Chaos Part II: Biology Applications Lecture 10: Coupled Systems. Ilya Potapov Mathematics Department, TUT Room TD325 Foreword In order to model populations of physical/biological

More information

arxiv: v1 [nlin.cd] 4 Dec 2017

arxiv: v1 [nlin.cd] 4 Dec 2017 Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators R. Gopal a, V. K. Chandrasekar a,, D. V. Senthilkumar c,, A. Venkatesan d, M. Lakshmanan b a Centre for Nonlinear

More information

Neural Excitability in a Subcritical Hopf Oscillator with a Nonlinear Feedback

Neural Excitability in a Subcritical Hopf Oscillator with a Nonlinear Feedback Neural Excitability in a Subcritical Hopf Oscillator with a Nonlinear Feedback Gautam C Sethia and Abhijit Sen Institute for Plasma Research, Bhat, Gandhinagar 382 428, INDIA Motivation Neural Excitability

More information

arxiv: v1 [nlin.ao] 2 Mar 2018

arxiv: v1 [nlin.ao] 2 Mar 2018 Stable amplitude chimera states in a network of locally coupled Stuart-Landau oscillators K. Premalatha, V. K. Chandrasekar, 2 M. Senthilvelan, and M. Lakshmanan ) Centre for Nonlinear Dynamics, School

More information

Time delay control of symmetry-breaking primary and secondary oscillation death

Time delay control of symmetry-breaking primary and secondary oscillation death epl draft Time delay control of symmetry-breaking primary and secondary oscillation death A. Zakharova 1, I. Schneider 2, Y. N. Kyrychko 3, K. B. Blyuss 3, A. Koseska 4, B. Fiedler 2 and E. Schöll 1 1

More information

arxiv: v2 [nlin.cd] 19 Apr 2018

arxiv: v2 [nlin.cd] 19 Apr 2018 Transition from homogeneous to inhomogeneous limit cycles: Effect of local filtering in coupled oscillators TanmoyBanerjee 1 DebabrataBiswas 2 Debarati Ghosh 1 Biswabibek Bandyopadhyay 1 and JürgenKurths

More information

Phase Synchronization

Phase Synchronization Phase Synchronization Lecture by: Zhibin Guo Notes by: Xiang Fan May 10, 2016 1 Introduction For any mode or fluctuation, we always have where S(x, t) is phase. If a mode amplitude satisfies ϕ k = ϕ k

More information

Chimera states in networks of biological neurons and coupled damped pendulums

Chimera states in networks of biological neurons and coupled damped pendulums in neural models in networks of pendulum-like elements in networks of biological neurons and coupled damped pendulums J. Hizanidis 1, V. Kanas 2, A. Bezerianos 3, and T. Bountis 4 1 National Center for

More information

Chimera State Realization in Chaotic Systems. The Role of Hyperbolicity

Chimera State Realization in Chaotic Systems. The Role of Hyperbolicity Chimera State Realization in Chaotic Systems. The Role of Hyperbolicity Vadim S. Anishchenko Saratov State University, Saratov, Russia Nizhny Novgorod, July 20, 2015 My co-authors Nadezhda Semenova, PhD

More information

Dynamics of slow and fast systems on complex networks

Dynamics of slow and fast systems on complex networks Indian Academy of Sciences Conference Series (2017) 1:1 DOI: 10.29195/iascs.01.01.0003 Indian Academy of Sciences Dynamics of slow and fast systems on complex networks KAJARI GUPTA and G. AMBIKA * Indian

More information

Dynamics and Patterns in Sheared Granular Fluid : Order Parameter Description and Bifurcation Scenario

Dynamics and Patterns in Sheared Granular Fluid : Order Parameter Description and Bifurcation Scenario Dynamics and Patterns in Sheared Granular Fluid : Order Parameter Description and Bifurcation Scenario NDAMS Workshop @ YITP 1 st November 2011 Meheboob Alam and Priyanka Shukla Engineering Mechanics Unit

More information

arxiv: v1 [nlin.cd] 23 Nov 2015

arxiv: v1 [nlin.cd] 23 Nov 2015 Different kinds of chimera death states in nonlocally coupled oscillators K. Premalatha 1, V. K. Chandrasekar 2, M. Senthilvelan 1, M. Lakshmanan 1 1 Centre for Nonlinear Dynamics, School of Physics, Bharathidasan

More information

arxiv: v2 [nlin.cd] 8 Nov 2017

arxiv: v2 [nlin.cd] 8 Nov 2017 Non-identical multiplexing promotes chimera states Saptarshi Ghosh a, Anna Zakharova b, Sarika Jalan a a Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore, Simrol, Indore

More information

Collective behavior in networks of biological neurons: mathematical modeling and software development

Collective behavior in networks of biological neurons: mathematical modeling and software development RESEARCH PROJECTS 2014 Collective behavior in networks of biological neurons: mathematical modeling and software development Ioanna Chitzanidi, Postdoctoral Researcher National Center for Scientific Research

More information

Stochastic resonance in the absence and presence of external signals for a chemical reaction

Stochastic resonance in the absence and presence of external signals for a chemical reaction JOURNAL OF CHEMICAL PHYSICS VOLUME 110, NUMBER 7 15 FEBRUARY 1999 Stochastic resonance in the absence and presence of external signals for a chemical reaction Lingfa Yang, Zhonghuai Hou, and Houwen Xin

More information

Krauskopf, B., Erzgraber, H., & Lenstra, D. (2006). Dynamics of semiconductor lasers with filtered optical feedback.

Krauskopf, B., Erzgraber, H., & Lenstra, D. (2006). Dynamics of semiconductor lasers with filtered optical feedback. Krauskopf, B, Erzgraber, H, & Lenstra, D (26) Dynamics of semiconductor lasers with filtered optical feedback Early version, also known as pre-print Link to publication record in Explore Bristol Research

More information

arxiv:chao-dyn/ v1 5 Mar 1996

arxiv:chao-dyn/ v1 5 Mar 1996 Turbulence in Globally Coupled Maps M. G. Cosenza and A. Parravano Centro de Astrofísica Teórica, Facultad de Ciencias, Universidad de Los Andes, A. Postal 26 La Hechicera, Mérida 5251, Venezuela (To appear,

More information

arxiv: v1 [nlin.cd] 20 Jul 2013

arxiv: v1 [nlin.cd] 20 Jul 2013 International Journal of Bifurcation and Chaos c World Scientific Publishing Company Chimera states in networs of nonlocally coupled Hindmarsh-Rose neuron models arxiv:37.545v [nlin.cd] Jul 3 Johanne Hizanidis

More information

University of Bristol - Explore Bristol Research. Early version, also known as pre-print

University of Bristol - Explore Bristol Research. Early version, also known as pre-print Erzgraber, H, Krauskopf, B, & Lenstra, D (2004) Compound laser modes of mutually delay-coupled lasers : bifurcation analysis of the locking region Early version, also known as pre-print Link to publication

More information

Synchronization Transitions in Complex Networks

Synchronization Transitions in Complex Networks Synchronization Transitions in Complex Networks Y. Moreno 1,2,3 1 Institute for Biocomputation and Physics of Complex Systems (BIFI) University of Zaragoza, Zaragoza 50018, Spain 2 Department of Theoretical

More information

DR. DIBAKAR GHOSH. Assistant Professor. Physics and Applied Mathematics Unit. Indian Statistical Institute

DR. DIBAKAR GHOSH. Assistant Professor. Physics and Applied Mathematics Unit. Indian Statistical Institute DR. DIBAKAR GHOSH Assistant Professor Physics and Applied Mathematics Unit Indian Statistical Institute 203 B. T. Road, Kolkata 700108, India. Mobile: +91-9830334136 E-Mail: diba.ghosh@gmail.com dibakar@isical.ac.in

More information

Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems. Davide Rossini. Scuola Normale Superiore, Pisa (Italy)

Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems. Davide Rossini. Scuola Normale Superiore, Pisa (Italy) Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems Davide Rossini Scuola Normale Superiore, Pisa (Italy) Quantum simulations and many-body physics with light Orthodox

More information

Strange dynamics of bilinear oscillator close to grazing

Strange dynamics of bilinear oscillator close to grazing Strange dynamics of bilinear oscillator close to grazing Ekaterina Pavlovskaia, James Ing, Soumitro Banerjee and Marian Wiercigroch Centre for Applied Dynamics Research, School of Engineering, King s College,

More information

Problem Set Number 2, j/2.036j MIT (Fall 2014)

Problem Set Number 2, j/2.036j MIT (Fall 2014) Problem Set Number 2, 18.385j/2.036j MIT (Fall 2014) Rodolfo R. Rosales (MIT, Math. Dept.,Cambridge, MA 02139) Due Mon., September 29, 2014. 1 Inverse function problem #01. Statement: Inverse function

More information

Modelling biological oscillations

Modelling biological oscillations Modelling biological oscillations Shan He School for Computational Science University of Birmingham Module 06-23836: Computational Modelling with MATLAB Outline Outline of Topics Van der Pol equation Van

More information

arxiv: v1 [nlin.ao] 19 May 2017

arxiv: v1 [nlin.ao] 19 May 2017 Feature-rich bifurcations in a simple electronic circuit Debdipta Goswami 1, and Subhankar Ray 2, 1 Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA

More information

DESYNCHRONIZATION TRANSITIONS IN RINGS OF COUPLED CHAOTIC OSCILLATORS

DESYNCHRONIZATION TRANSITIONS IN RINGS OF COUPLED CHAOTIC OSCILLATORS Letters International Journal of Bifurcation and Chaos, Vol. 8, No. 8 (1998) 1733 1738 c World Scientific Publishing Company DESYNCHRONIZATION TRANSITIONS IN RINGS OF COUPLED CHAOTIC OSCILLATORS I. P.

More information

The Hopf-van der Pol System: Failure of a Homotopy Method

The Hopf-van der Pol System: Failure of a Homotopy Method DOI.7/s259--9-5 ORIGINAL RESEARCH The Hopf-van der Pol System: Failure of a Homotopy Method H. G. E. Meijer T. Kalmár-Nagy Foundation for Scientific Research and Technological Innovation 2 Abstract The

More information

Phase Synchronization of Coupled Rossler Oscillators: Amplitude Effect

Phase Synchronization of Coupled Rossler Oscillators: Amplitude Effect Commun. Theor. Phys. (Beijing, China) 47 (2007) pp. 265 269 c International Academic Publishers Vol. 47, No. 2, February 15, 2007 Phase Synchronization of Coupled Rossler Oscillators: Amplitude Effect

More information

Complex Patterns in a Simple System

Complex Patterns in a Simple System Complex Patterns in a Simple System arxiv:patt-sol/9304003v1 17 Apr 1993 John E. Pearson Center for Nonlinear Studies Los Alamos National Laboratory February 4, 2008 Abstract Numerical simulations of a

More information

7 Two-dimensional bifurcations

7 Two-dimensional bifurcations 7 Two-dimensional bifurcations As in one-dimensional systems: fixed points may be created, destroyed, or change stability as parameters are varied (change of topological equivalence ). In addition closed

More information

Period-doubling cascades of a Silnikov equation

Period-doubling cascades of a Silnikov equation Period-doubling cascades of a Silnikov equation Keying Guan and Beiye Feng Science College, Beijing Jiaotong University, Email: keying.guan@gmail.com Institute of Applied Mathematics, Academia Sinica,

More information

Oscillatory Turing Patterns in a Simple Reaction-Diffusion System

Oscillatory Turing Patterns in a Simple Reaction-Diffusion System Journal of the Korean Physical Society, Vol. 50, No. 1, January 2007, pp. 234 238 Oscillatory Turing Patterns in a Simple Reaction-Diffusion System Ruey-Tarng Liu and Sy-Sang Liaw Department of Physics,

More information

PHASE-LOCKED SOLUTIONS IN A HUB CONNECTED OSCILLATOR RING NETWORK

PHASE-LOCKED SOLUTIONS IN A HUB CONNECTED OSCILLATOR RING NETWORK Copyright c 29 by ABCM PHASE-LOCKED SOLUTIONS IN A HUB CONNECTED OSCILLATOR RING NETWORK Jacqueline Bridge, Jacqueline.Bridge@sta.uwi.edu Department of Mechanical Engineering, The University of the West

More information

Difference Resonances in a controlled van der Pol-Duffing oscillator involving time. delay

Difference Resonances in a controlled van der Pol-Duffing oscillator involving time. delay Difference Resonances in a controlled van der Pol-Duffing oscillator involving time delay This paper was published in the journal Chaos, Solitions & Fractals, vol.4, no., pp.975-98, Oct 9 J.C. Ji, N. Zhang,

More information

Oscillation death in a coupled van der Pol Mathieu system

Oscillation death in a coupled van der Pol Mathieu system PRAMANA c Indian Academy of Sciences Vol. 81, No. 4 journal of October 2013 physics pp. 677 690 Oscillation death in a coupled van der Pol Mathieu system MADHURJYA P BORA and DIPAK SARMAH Physics Department,

More information

Hysteretic Transitions in the Kuramoto Model with Inertia

Hysteretic Transitions in the Kuramoto Model with Inertia Rostock 4 p. Hysteretic Transitions in the uramoto Model with Inertia A. Torcini, S. Olmi, A. Navas, S. Boccaletti http://neuro.fi.isc.cnr.it/ Istituto dei Sistemi Complessi - CNR - Firenze, Italy Istituto

More information

Additive resonances of a controlled van der Pol-Duffing oscillator

Additive resonances of a controlled van der Pol-Duffing oscillator Additive resonances of a controlled van der Pol-Duffing oscillator This paper has been published in Journal of Sound and Vibration vol. 5 issue - 8 pp.-. J.C. Ji N. Zhang Faculty of Engineering University

More information

Dynamics of delayed-coupled chaotic logistic maps: Influence of network topology, connectivity and delay times

Dynamics of delayed-coupled chaotic logistic maps: Influence of network topology, connectivity and delay times PRAMANA c Indian Academy of Sciences Vol. 7, No. 6 journal of June 28 physics pp. 1 9 Dynamics of delayed-coupled chaotic logistic maps: Influence of network topology, connectivity and delay times ARTURO

More information

TWO DIMENSIONAL FLOWS. Lecture 5: Limit Cycles and Bifurcations

TWO DIMENSIONAL FLOWS. Lecture 5: Limit Cycles and Bifurcations TWO DIMENSIONAL FLOWS Lecture 5: Limit Cycles and Bifurcations 5. Limit cycles A limit cycle is an isolated closed trajectory [ isolated means that neighbouring trajectories are not closed] Fig. 5.1.1

More information

Random Averaging. Eli Ben-Naim Los Alamos National Laboratory. Paul Krapivsky (Boston University) John Machta (University of Massachusetts)

Random Averaging. Eli Ben-Naim Los Alamos National Laboratory. Paul Krapivsky (Boston University) John Machta (University of Massachusetts) Random Averaging Eli Ben-Naim Los Alamos National Laboratory Paul Krapivsky (Boston University) John Machta (University of Massachusetts) Talk, papers available from: http://cnls.lanl.gov/~ebn Plan I.

More information

Self-Replication, Self-Destruction, and Spatio-Temporal Chaos in the Gray-Scott Model

Self-Replication, Self-Destruction, and Spatio-Temporal Chaos in the Gray-Scott Model Letter Forma, 15, 281 289, 2000 Self-Replication, Self-Destruction, and Spatio-Temporal Chaos in the Gray-Scott Model Yasumasa NISHIURA 1 * and Daishin UEYAMA 2 1 Laboratory of Nonlinear Studies and Computations,

More information

STUDY OF SYNCHRONIZED MOTIONS IN A ONE-DIMENSIONAL ARRAY OF COUPLED CHAOTIC CIRCUITS

STUDY OF SYNCHRONIZED MOTIONS IN A ONE-DIMENSIONAL ARRAY OF COUPLED CHAOTIC CIRCUITS International Journal of Bifurcation and Chaos, Vol 9, No 11 (1999) 19 4 c World Scientific Publishing Company STUDY OF SYNCHRONIZED MOTIONS IN A ONE-DIMENSIONAL ARRAY OF COUPLED CHAOTIC CIRCUITS ZBIGNIEW

More information

Numerical techniques: Deterministic Dynamical Systems

Numerical techniques: Deterministic Dynamical Systems Numerical techniques: Deterministic Dynamical Systems Henk Dijkstra Institute for Marine and Atmospheric research Utrecht, Department of Physics and Astronomy, Utrecht, The Netherlands Transition behavior

More information

arxiv: v1 [nlin.cd] 3 Dec 2014

arxiv: v1 [nlin.cd] 3 Dec 2014 Time-delayed feedback control of coherence resonance near subcritical Hopf bifurcation: theory versus experiment Vladimir Semenov, Alexey Feoktistov, Tatyana Vadivasova, Eckehard Schöll,, a), b) and Anna

More information

SPATIOTEMPORAL CHAOS IN COUPLED MAP LATTICE. Itishree Priyadarshini. Prof. Biplab Ganguli

SPATIOTEMPORAL CHAOS IN COUPLED MAP LATTICE. Itishree Priyadarshini. Prof. Biplab Ganguli SPATIOTEMPORAL CHAOS IN COUPLED MAP LATTICE By Itishree Priyadarshini Under the Guidance of Prof. Biplab Ganguli Department of Physics National Institute of Technology, Rourkela CERTIFICATE This is to

More information

Chapter 24 BIFURCATIONS

Chapter 24 BIFURCATIONS Chapter 24 BIFURCATIONS Abstract Keywords: Phase Portrait Fixed Point Saddle-Node Bifurcation Diagram Codimension-1 Hysteresis Hopf Bifurcation SNIC Page 1 24.1 Introduction In linear systems, responses

More information

Thermoacoustic Instabilities Research

Thermoacoustic Instabilities Research Chapter 3 Thermoacoustic Instabilities Research In this chapter, relevant literature survey of thermoacoustic instabilities research is included. An introduction to the phenomena of thermoacoustic instability

More information

2 Discrete growth models, logistic map (Murray, Chapter 2)

2 Discrete growth models, logistic map (Murray, Chapter 2) 2 Discrete growth models, logistic map (Murray, Chapter 2) As argued in Lecture 1 the population of non-overlapping generations can be modelled as a discrete dynamical system. This is an example of an

More information

Clearly the passage of an eigenvalue through to the positive real half plane leads to a qualitative change in the phase portrait, i.e.

Clearly the passage of an eigenvalue through to the positive real half plane leads to a qualitative change in the phase portrait, i.e. Bifurcations We have already seen how the loss of stiffness in a linear oscillator leads to instability. In a practical situation the stiffness may not degrade in a linear fashion, and instability may

More information

3.5 Competition Models: Principle of Competitive Exclusion

3.5 Competition Models: Principle of Competitive Exclusion 94 3. Models for Interacting Populations different dimensional parameter changes. For example, doubling the carrying capacity K is exactly equivalent to halving the predator response parameter D. The dimensionless

More information

Saturation of Information Exchange in Locally Connected Pulse-Coupled Oscillators

Saturation of Information Exchange in Locally Connected Pulse-Coupled Oscillators Saturation of Information Exchange in Locally Connected Pulse-Coupled Oscillators Will Wagstaff School of Computer Science, Georgia Institute of Technology, Atlanta, Georgia 30332, USA (Dated: 13 December

More information

Lecture 3 : Bifurcation Analysis

Lecture 3 : Bifurcation Analysis Lecture 3 : Bifurcation Analysis D. Sumpter & S.C. Nicolis October - December 2008 D. Sumpter & S.C. Nicolis General settings 4 basic bifurcations (as long as there is only one unstable mode!) steady state

More information

Hysteresis. Lab 6. Recall that any ordinary differential equation can be written as a first order system of ODEs,

Hysteresis. Lab 6. Recall that any ordinary differential equation can be written as a first order system of ODEs, Lab 6 Hysteresis Recall that any ordinary differential equation can be written as a first order system of ODEs, ẋ = F (x), ẋ := d x(t). (6.1) dt Many interesting applications and physical phenomena can

More information

Kristina Lerman USC Information Sciences Institute

Kristina Lerman USC Information Sciences Institute Rethinking Network Structure Kristina Lerman USC Information Sciences Institute Università della Svizzera Italiana, December 16, 2011 Measuring network structure Central nodes Community structure Strength

More information

Symmetry Properties of Confined Convective States

Symmetry Properties of Confined Convective States Symmetry Properties of Confined Convective States John Guckenheimer Cornell University 1 Introduction This paper is a commentary on the experimental observation observations of Bensimon et al. [1] of convection

More information

Emergent Phenomena on Complex Networks

Emergent Phenomena on Complex Networks Chapter 1 Emergent Phenomena on Complex Networks 1.0.1 More is different When many interacting elements give rise to a collective behavior that cannot be explained or predicted by considering them individually,

More information

Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber

Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber J.C. Ji, N. Zhang Faculty of Engineering, University of Technology, Sydney PO Box, Broadway,

More information

Numerical Study on the Quasi-periodic Behavior in Coupled. MEMS Resonators

Numerical Study on the Quasi-periodic Behavior in Coupled. MEMS Resonators THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE. Numerical Study on the Quasi-periodic Behavior in Coupled Abstract MEMS Resonators Suketu NAIK and Takashi

More information

MULTISTABILITY IN A BUTTERFLY FLOW

MULTISTABILITY IN A BUTTERFLY FLOW International Journal of Bifurcation and Chaos, Vol. 23, No. 12 (2013) 1350199 (10 pages) c World Scientific Publishing Company DOI: 10.1142/S021812741350199X MULTISTABILITY IN A BUTTERFLY FLOW CHUNBIAO

More information

Spatiotemporal pattern formation in a prey-predator model under environmental driving forces

Spatiotemporal pattern formation in a prey-predator model under environmental driving forces Home Search Collections Journals About Contact us My IOPscience Spatiotemporal pattern formation in a prey-predator model under environmental driving forces This content has been downloaded from IOPscience.

More information

arxiv: v1 [cond-mat.stat-mech] 6 Mar 2008

arxiv: v1 [cond-mat.stat-mech] 6 Mar 2008 CD2dBS-v2 Convergence dynamics of 2-dimensional isotropic and anisotropic Bak-Sneppen models Burhan Bakar and Ugur Tirnakli Department of Physics, Faculty of Science, Ege University, 35100 Izmir, Turkey

More information

Self-organized Criticality and Synchronization in a Pulse-coupled Integrate-and-Fire Neuron Model Based on Small World Networks

Self-organized Criticality and Synchronization in a Pulse-coupled Integrate-and-Fire Neuron Model Based on Small World Networks Commun. Theor. Phys. (Beijing, China) 43 (2005) pp. 466 470 c International Academic Publishers Vol. 43, No. 3, March 15, 2005 Self-organized Criticality and Synchronization in a Pulse-coupled Integrate-and-Fire

More information

A theory for one dimensional asynchronous waves observed in nonlinear dynamical systems

A theory for one dimensional asynchronous waves observed in nonlinear dynamical systems A theory for one dimensional asynchronous waves oserved in nonlinear dynamical systems arxiv:nlin/0510071v1 [nlin.ps] 28 Oct 2005 A. Bhattacharyay Dipartimento di Fisika G. Galilei Universitá di Padova

More information

Magnetic waves in a two-component model of galactic dynamo: metastability and stochastic generation

Magnetic waves in a two-component model of galactic dynamo: metastability and stochastic generation Center for Turbulence Research Annual Research Briefs 006 363 Magnetic waves in a two-component model of galactic dynamo: metastability and stochastic generation By S. Fedotov AND S. Abarzhi 1. Motivation

More information

ONE DIMENSIONAL FLOWS. Lecture 3: Bifurcations

ONE DIMENSIONAL FLOWS. Lecture 3: Bifurcations ONE DIMENSIONAL FLOWS Lecture 3: Bifurcations 3. Bifurcations Here we show that, although the dynamics of one-dimensional systems is very limited [all solutions either settle down to a steady equilibrium

More information

Synchronization of Limit Cycle Oscillators by Telegraph Noise. arxiv: v1 [cond-mat.stat-mech] 5 Aug 2014

Synchronization of Limit Cycle Oscillators by Telegraph Noise. arxiv: v1 [cond-mat.stat-mech] 5 Aug 2014 Synchronization of Limit Cycle Oscillators by Telegraph Noise Denis S. Goldobin arxiv:148.135v1 [cond-mat.stat-mech] 5 Aug 214 Department of Physics, University of Potsdam, Postfach 61553, D-14415 Potsdam,

More information

DYNAMICS OF THREE COUPLED VAN DER POL OSCILLATORS WITH APPLICATION TO CIRCADIAN RHYTHMS

DYNAMICS OF THREE COUPLED VAN DER POL OSCILLATORS WITH APPLICATION TO CIRCADIAN RHYTHMS Proceedings of IDETC/CIE 2005 ASME 2005 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference September 24-28, 2005, Long Beach, California USA DETC2005-84017

More information

1D spirals: is multi stability essential?

1D spirals: is multi stability essential? 1D spirals: is multi staility essential? A. Bhattacharyay Dipartimento di Fisika G. Galilei Universitá di Padova Via Marzolo 8, 35131 Padova Italy arxiv:nlin/0502024v2 [nlin.ps] 23 Sep 2005 Feruary 8,

More information

arxiv: v1 [physics.ao-ph] 23 May 2017

arxiv: v1 [physics.ao-ph] 23 May 2017 Effect of Heterogeneity in Models of El-Niño Southern Oscillations Chandrakala Meena a, Shweta Kumari b, Akansha Sharma c, 2 and Sudeshna Sinha d Indian Institute of Science Education and Research (IISER)

More information

Analytic Solution for a Complex Network of Chaotic Oscillators

Analytic Solution for a Complex Network of Chaotic Oscillators Article Analytic Solution for a Complex Network of Chaotic Oscillators Jonathan N. Blakely * ID, Marko S. Milosavljevic and Ned J. Corron Charles M. Bowden Laboratory, U. S. Army Aviation and Missile Research,

More information

CHEM 515: Chemical Kinetics and Dynamics

CHEM 515: Chemical Kinetics and Dynamics Alejandro J. Garza S01163018 Department of Chemistry, Rice University, Houston, TX email: ajg7@rice.edu, ext. 2657 Submitted December 12, 2011 Abstract Spontaneous antispiral wave formation was observed

More information

One Dimensional Dynamical Systems

One Dimensional Dynamical Systems 16 CHAPTER 2 One Dimensional Dynamical Systems We begin by analyzing some dynamical systems with one-dimensional phase spaces, and in particular their bifurcations. All equations in this Chapter are scalar

More information

Complete Synchronization, Anti-synchronization and Hybrid Synchronization Between Two Different 4D Nonlinear Dynamical Systems

Complete Synchronization, Anti-synchronization and Hybrid Synchronization Between Two Different 4D Nonlinear Dynamical Systems Mathematics Letters 2016; 2(5): 36-41 http://www.sciencepublishinggroup.com/j/ml doi: 10.11648/j.ml.20160205.12 Complete Synchronization, Anti-synchronization and Hybrid Synchronization Between Two Different

More information

Growth oscillations. LElTER TO THE EDITOR. Zheming Cheng and Robert Savit

Growth oscillations. LElTER TO THE EDITOR. Zheming Cheng and Robert Savit J. Phys. A: Math. Gen. 19 (1986) L973-L978. Printed in Great Britain LElTER TO THE EDITOR Growth oscillations Zheming Cheng and Robert Savit Department of Physics, The University of Michigan, Ann Arbor,

More information

CHAPTER 6 HOPF-BIFURCATION IN A TWO DIMENSIONAL NONLINEAR DIFFERENTIAL EQUATION

CHAPTER 6 HOPF-BIFURCATION IN A TWO DIMENSIONAL NONLINEAR DIFFERENTIAL EQUATION CHAPTER 6 HOPF-BIFURCATION IN A TWO DIMENSIONAL NONLINEAR DIFFERENTIAL EQUATION [Discussion on this chapter is based on our paper entitled Hopf-Bifurcation Ina Two Dimensional Nonlinear Differential Equation,

More information

Phase Locking. 1 of of 10. The PRC's amplitude determines which frequencies a neuron locks to. The PRC's slope determines if locking is stable

Phase Locking. 1 of of 10. The PRC's amplitude determines which frequencies a neuron locks to. The PRC's slope determines if locking is stable Printed from the Mathematica Help Browser 1 1 of 10 Phase Locking A neuron phase-locks to a periodic input it spikes at a fixed delay [Izhikevich07]. The PRC's amplitude determines which frequencies a

More information

Time-periodic forcing of Turing patterns in the Brusselator model

Time-periodic forcing of Turing patterns in the Brusselator model Time-periodic forcing of Turing patterns in the Brusselator model B. Peña and C. Pérez García Instituto de Física. Universidad de Navarra, Irunlarrea, 1. 31008-Pamplona, Spain Abstract Experiments on temporal

More information

Optical Self-Organization in Semiconductor Lasers Spatio-temporal Dynamics for All-Optical Processing

Optical Self-Organization in Semiconductor Lasers Spatio-temporal Dynamics for All-Optical Processing Optical Self-Organization in Semiconductor Lasers Spatio-temporal Dynamics for All-Optical Processing Self-Organization for all-optical processing What is at stake? Cavity solitons have a double concern

More information

Analysis and Simulation of Biological Systems

Analysis and Simulation of Biological Systems Analysis and Simulation of Biological Systems Dr. Carlo Cosentino School of Computer and Biomedical Engineering Department of Experimental and Clinical Medicine Università degli Studi Magna Graecia Catanzaro,

More information

Antimonotonicity in Chua s Canonical Circuit with a Smooth Nonlinearity

Antimonotonicity in Chua s Canonical Circuit with a Smooth Nonlinearity Antimonotonicity in Chua s Canonical Circuit with a Smooth Nonlinearity IOANNIS Μ. KYPRIANIDIS & MARIA Ε. FOTIADOU Physics Department Aristotle University of Thessaloniki Thessaloniki, 54124 GREECE Abstract:

More information

Common noise induces clustering in populations of globally coupled oscillators

Common noise induces clustering in populations of globally coupled oscillators OFFPRINT Common noise induces clustering in populations of globally coupled oscillators S. Gil, Y. Kuramoto and A. S. Mikhailov EPL, 88 (29) 65 Please visit the new website www.epljournal.org TARGET YOUR

More information

SELF-ORGANIZATION IN NONRECURRENT COMPLEX SYSTEMS

SELF-ORGANIZATION IN NONRECURRENT COMPLEX SYSTEMS Letters International Journal of Bifurcation and Chaos, Vol. 10, No. 5 (2000) 1115 1125 c World Scientific Publishing Company SELF-ORGANIZATION IN NONRECURRENT COMPLEX SYSTEMS PAOLO ARENA, RICCARDO CAPONETTO,

More information

Time Delays in Neural Systems

Time Delays in Neural Systems Time Delays in Neural Systems Sue Ann Campbell 1 Department of Applied Mathematics, University of Waterloo, Waterloo ON N2l 3G1 Canada sacampbell@uwaterloo.ca Centre for Nonlinear Dynamics in Physiology

More information

Dynamics of Modified Leslie-Gower Predator-Prey Model with Predator Harvesting

Dynamics of Modified Leslie-Gower Predator-Prey Model with Predator Harvesting International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:13 No:05 55 Dynamics of Modified Leslie-Gower Predator-Prey Model with Predator Harvesting K. Saleh Department of Mathematics, King Fahd

More information

arxiv: v4 [nlin.cd] 20 Feb 2014

arxiv: v4 [nlin.cd] 20 Feb 2014 EPJ manuscript No. (will be inserted by the editor) Chimera States in a Two Population Network of Coupled Pendulum Like Elements Tassos Bountis 1,a, Vasileios G. Kanas, Johanne Hizanidis 3, and Anastasios

More information

Length Scales Related to Alpha and Beta Relaxation in Glass Forming Liquids

Length Scales Related to Alpha and Beta Relaxation in Glass Forming Liquids Length Scales Related to Alpha and Beta Relaxation in Glass Forming Liquids Chandan Dasgupta Centre for Condensed Matter Theory Department of Physics, Indian Institute of Science With Smarajit Karmakar

More information

Motivation. Evolution has rediscovered several times multicellularity as a way to build complex living systems

Motivation. Evolution has rediscovered several times multicellularity as a way to build complex living systems Cellular Systems 1 Motivation Evolution has rediscovered several times multicellularity as a way to build complex living systems Multicellular systems are composed by many copies of a unique fundamental

More information

Coherence of Noisy Oscillators with Delayed Feedback Inducing Multistability

Coherence of Noisy Oscillators with Delayed Feedback Inducing Multistability Journal of Physics: Conference Series PAPER OPEN ACCESS Coherence of Noisy Oscillators with Delayed Feedback Inducing Multistability To cite this article: Anastasiya V Pimenova and Denis S Goldobin 2016

More information

Competition of Spatial and Temporal Instabilities under Time Delay near Codimension-Two Turing Hopf Bifurcations

Competition of Spatial and Temporal Instabilities under Time Delay near Codimension-Two Turing Hopf Bifurcations Commun. Theor. Phys. 56 (2011) 339 344 Vol. 56, No. 2, August 15, 2011 Competition of Spatial and Temporal Instabilities under Time Delay near Codimension-Two Turing Hopf Bifurcations WANG Hui-Juan ( )

More information

The Role of Retinoic Acid and Notch in the Symmetry Breaking Instabilities for Axon Formation

The Role of Retinoic Acid and Notch in the Symmetry Breaking Instabilities for Axon Formation The Role of Retinoic Acid and Notch in the Symmetry Breaking Instabilities for Axon Formation MAJID BANI-YAGHOB DAVID E. AMNDSEN School of Mathematics and Statistics, Carleton niversity 1125 Colonel By

More information

Introduction to bifurcations

Introduction to bifurcations Introduction to bifurcations Marc R. Roussel September 6, Introduction Most dynamical systems contain parameters in addition to variables. A general system of ordinary differential equations (ODEs) could

More information

arxiv: v2 [physics.optics] 15 Dec 2016

arxiv: v2 [physics.optics] 15 Dec 2016 Bifurcation analysis of the Yamada model for a pulsing semiconductor laser with saturable absorber and delayed optical feedback Abstract Soizic Terrien 1, Bernd Krauskopf 1, Neil G.R. Broderick 2 arxiv:1610.06794v2

More information

Chaos & Recursive. Ehsan Tahami. (Properties, Dynamics, and Applications ) PHD student of biomedical engineering

Chaos & Recursive. Ehsan Tahami. (Properties, Dynamics, and Applications ) PHD student of biomedical engineering Chaos & Recursive Equations (Properties, Dynamics, and Applications ) Ehsan Tahami PHD student of biomedical engineering Tahami@mshdiau.a.ir Index What is Chaos theory? History of Chaos Introduction of

More information

2 1. Introduction. Neuronal networks often exhibit a rich variety of oscillatory behavior. The dynamics of even a single cell may be quite complicated

2 1. Introduction. Neuronal networks often exhibit a rich variety of oscillatory behavior. The dynamics of even a single cell may be quite complicated GEOMETRIC ANALYSIS OF POPULATION RHYTHMS IN SYNAPTICALLY COUPLED NEURONAL NETWORKS J. Rubin and D. Terman Dept. of Mathematics; Ohio State University; Columbus, Ohio 43210 Abstract We develop geometric

More information

Resonant suppression of Turing patterns by periodic illumination

Resonant suppression of Turing patterns by periodic illumination PHYSICAL REVIEW E, VOLUME 63, 026101 Resonant suppression of Turing patterns by periodic illumination Milos Dolnik,* Anatol M. Zhabotinsky, and Irving R. Epstein Department of Chemistry and Volen Center

More information