Synchronization in Populations of Chemical Oscillators

Transcription

1 Synchronization in Populations of Chemical Oscillators Advanced Computational and Experimental Techniques in Nonlinear Dynamics February 20-24, 2012 Puebla, Mexico Co-Workers: Annette Taylor Mark Tinsley Zhaoyang Huang Fang Wang Simba Nkomo Funding: NSF

2 Catalyst-Loaded Beads in Catalyst-Free BZ Solution Exchange species: X = HBrO 2 Y = Br - Immobilized: Z = Fe(phen) 3 3+ Desynchronization transition with decreasing density for a particular exchange rate: globally oscillatory to globally nonoscillatory (with oscillatory individuals). R. Toth, A. F. Taylor, and M. R. Tinsley, J. Phys. Chem. B 110, (2006). J. Maselko and K. Showalter, Nature 339, 609 (1989) Large populations! A cuvette 1.8 cm 1.8 cm allows a population of about 100,000 catalyst-loaded ~200 μm beads.

3 Experimental Setup Stirred suspension of catalyst-loaded particles in catalyst-free solution Particle size: ~200 μm Stirring rate: rpm Shutter speed: 0.4 ms Frame rate: 1 s Video Pt electrode A. F. Taylor, M. R. Tinsley, F. Wang, Z. Huang, KS, Science 323, 614 (2009).

4 Transition at Low Exchange Rate Stirring speed: 300 rpm Catalyst particle density g/ml, g/ml, g/ml, g/ml, g/ml, g/ml, g/ml.

5 Transition at High Exchange Rate Pt electrode potential vs time Stirring rate = 600 rpm

6 Global Signal: Amplitude of Variable X S b(i) k = 3 s -1, b(ii) k = 0.3 s -1 Amplitude of HBrO 2 in solution. c(i) n = 8200 cm -3, c(ii) n = 4200 cm -3

7 Clusters in the Globally Coupled System Ru(bpy) 2+ 3 System Clusters: groups of oscillators within a population of oscillators that have different phases but (generally) the same frequency. Complex global signals arise -- composite of the individual cluster signals. Distribution of cluster oscillator populations dependent on initial conditions. Reaction mixture composition: [NaBrO 3 ] = 0.41 M, [NaBr] = 0.07 M, [MA] = 0.14 M, [H 2 SO 4 ] = 0.68 M Particle catalyst loading: Ru(bpy) 3 2+ = mol g -1 I. Z. Kiss, Y. Zhai, J. L. Hudson, Science 296, 1676 (2002). I. Z. Kiss, Y. Zhai, J. L. Hudson, Phys. Rev. Lett. 94, (2005). A. F. Taylor et al., Phys. Rev. Lett. 100, (2008).

8 Synchronized One-Cluster, Two-Cluster 2-Cluster 1-Cluster A. F. Taylor, M. R. Tinsley, F. Wang, KS, Angewandte Chemie Int. Ed. (2011).

9 Unsynchronized No Cluster Behavior Sampling (100) of 400 globally coupled oscillators n = 4,000 cm -3 K ex = 0.9 s -1 C = 2.0 x 10-2 M Time series of global signal of Br - concentration. Flat signal from unsynchronized oscillators.

10 Unsynchronized No Cluster Behavior Phase plot and period distribution for n = 4,000 cm -3 and K ex = 0.9 s -1 Time series for oscillators with natural periods of 26 s, 30 s, 23 s. θ = 2π(t t n )/(t n+1 t n ); x = sinθ, y = cosθ

11 Synchronized (almost) Four Clusters Sampling (100) of 800 globally coupled oscillators n = 8,000 cm -3 K ex = 0.9 s -1 C = 2.0 x 10-2 M Time series of global signal of Br - concentration. Four successively smaller oscillations per period.

12 Synchronized (almost) Four Clusters Phase plot and period distribution for n = 8,000 cm -3 and K ex = 0.9 s -1 Time series for oscillators with natural periods of 26 s, 30 s, 23 s.

13 Two Unequal Clusters Sampling (100) of 3200 globally coupled oscillators n = 32,000 cm -3 K ex = 0.9 s -1 C = 2.0 x 10-2 M Time series of global signal of Br - concentration. One large and one small oscillation per period.

14 Phase plot and period distribution for n = 32,000 cm -3 and K ex = 0.9 s -1 Time series for oscillators with natural periods of 26 s, 30 s, 23 s. Two Unequal Clusters

15 Two Equal Clusters with Switchers Sampling (100) of 5200 globally coupled oscillators n = 52,000 cm -3 K ex = 0.9 s -1 C = 2.0 x 10-2 M Time series of global signal of Br - concentration. Similar but varying amplitudes.

16 Two Equal Clusters with Switchers Phase plot and period distribution for n = 52,000 cm -3 and K ex = 0.9 s -1 Time series for oscillators with natural periods of 26 s, 30 s, 23 s.

17 Synchronized One Cluster Sampling (100) of 2000 (with 0.1Vs) globally coupled oscillators n = 200,000 cm -3 K ex = 0.9 s -1 C = 2.0 x 10-2 M Time series of global signal of Br - concentration. Completely synchronized.

18 Phase plot and period distribution for n = 200,000 cm -3 and K ex = 0.9 s -1 Time series for oscillators with natural periods of 26 s, 30 s, 23 s. Synchronized One Cluster

19 Number of Clusters vs Exchange Rate and Number Density Unsynchronized to 4-cluster, 3-cluster, 2-cluster and 1-cluster (complete synchronization) on increasing n and/or k ex. No evidence of cluster state multi-stability. Many cluster states with different oscillator distributions. N = 1000

20 Population Density Dependent Behavior of Discrete Chemical Oscillators Globally Coupled System: Kuramoto Synchronization Quorum Sensing A.F. Taylor et al., Science 323, 614 (2009). Cluster Formation in Synchronization: Phase Clusters, Switchers and Cluster Transitions A. F. Taylor et al., Angewandte Chemie Int. Ed. (2011). Spatially Distributed System: Excitable Particle Dynamical Quorum Sensing M.R. Tinsley et al., Phys. Rev. Lett. 102, (2009).