Self-Organization and Collective Decision Making in Animal and Human Societies
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1 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March 26 1 / 23 Self-Organization and Collective Decision Making in Animal and Human Societies Frank Schweitzer fschweitzer@ethz.ch
2 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March 26 2 / 23 Animal societies Biological aggregation Example: Biological Aggregation cells, slime mold amoebae, myxobacteria generate a chemical field to communicate chemotaxis Deneubourg, J. L.; Gregoire, J. C.; Le Fort, E. (199): Kinetics of Larval Gregarious Behavior in the Bark Beetle Dendroctonus micans (Coleoptera: Scolytiadae), J. Insect Behavior 3/2, (199)
3 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March 26 3 / 23 Animal societies Biological aggregation Modeling approach: Brownian Agents variable: position r i, dynamics: generalized Langevin equation dr i dt = α h (r, t) i r + 2 D n ξ i (t) ri adaptive landscape: chemical field h (r, t) N t h (r, t) = s i δ(r r i ) k h (r, t) + D h (r, t) i=1 F.S., Brownian Agents and Active Particles. Collective Dynamics in the Natural and Social Sciences, Springer, 23 (42 pp., 192 illus.)
4 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March 26 4 / 23 Animal societies Biological aggregation indirect communication via adaptive landscape changes agent landscape influences
5 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March 26 5 / 23 Animal societies Biological aggregation Computer Simulations time: (top) 1 2, 1 3, 5 1 3, (bottom) 1 4, , 5 1 4
6 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March 26 6 / 23 Animal societies Biological aggregation Evolution of the adaptive landscape time: (top) 1 2, 1 3, 5 1 3, (bottom) 1 3, 5 1 3, Note that the vertical scale in the top row is 1 times the scale of the bottom row
7 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March 26 7 / 23 Animal societies Biological aggregation Summary: agents follow local rules, create global structures reason: nonlinear feedback between individual actions agents drive system into nonequilibrium: s two characteristic time scales for field dynamics: early: independent growth of spikes (many small clusters) late: competition of spikes for agents theoretical investigations (F.S., L. Schimansky-Geier, Physica A 26 (1994) ) derivation of a selection equation: survival of the fittest dx [ ] i dt = x i E i E i ; E i = i E i x i i x i derivation of an effective diffusion equation n(r, t) = { } n(r, t) D eff ; D eff = 1 ] [k B T α h (r, t) t r r γ
8 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March 26 8 / 23 Animal societies Foraging behavior in ants Example: Foraging Route of Ants Schematic representation of the complete foraging route of Pheidole milicida, a harvesting ant of the southwestern U.S. deserts. Each day tens of thousands of workers move out to the dendritic trail system, disperse singly, and forage for food. Hölldobler, B. and Möglich, M.: The foraging system of Pheidole militicida (Hymenoptera: Formicidae), Insectes Sociaux 27/3 (198)
9 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March 26 9 / 23 Animal societies Foraging behavior in ants Brownian Agents position r i, θ i { 1, +1} (found food or not) ω i {; 1} (scouts, recruits), sensitivity η i C -1 generates h (r,t) -1 influences C +1 influences generates h (r,t) +1 F.S., K. Lao, F. Family, BioSystems 41 (1997) Simulation
10 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March 26 1 / 23 Collective decision making Collective Decisions of Social Agents N agents: position r i IR 2, opinion θ i { 1, +1} binary choice: to change or to keep opinion θ { i w( θ i θ i ) = η exp h } θ(r i, t) h θ (r i, t) T herding behavior depends on information hθ (r i, t) about decisions of other agents η: defines time scale T : social temperature measures randomness of social interaction T : deterministic behavior
11 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March / 23 Collective decision making Spatio-temporal communication field t h θ(r, t) = N s i δ θ,θi δ(r r i ) k θ h θ (r, t) + D θ h θ (r, t) i=1 multi-component scalar field reflects: existence of memory (past experience) exchange of information with finite velocity influence of spatial distances between agents weighted influence (space, time)
12 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March / 23 Collective decision making non-linear feedback: generates generates C +1 h +1 (r,t), h -1 (r,t) C -1 } influences influences
13 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March / 23 Collective decision making Fast Information Exchange no spatial heterogeneity mean-field approach stat x κ κ = A 2s k N T = 2 critical population size: N c = k A s T Emergence of minority and majority
14 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March / 23 Spatial patterns Spatial Influences on Decisions s +1 = s 1 s, k +1 = k 1 k, D +1 = D 1 D t = 1
15 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March / 23 Spatial patterns t = 1 2
16 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March / 23 Spatial patterns t = 1 4
17 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March / 23 Spatial patterns Is the outcome determined? System size: A = 16, total number of agents: N = 16, time: t = 5 1 4, frequency: x + =.543
18 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March / 23 Spatial patterns almost every minority/majority relation may be established <x > t dependence on information dissemination (D), memory (k), agent density (N/A)
19 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March / 23 Multi-attractor regime Analytical Investigations impact of information κ = 2ν/T : relation between net information density ν = n s/k and efficiency 1/T existence of two bifurcations: κ > κ 1 = 2: minority/majority κ > κ 2 (D/k): multi-attractor regime 8 κ i multi attractor regime κ single attractor regime κ 2 1 no majority/minority D/k
20 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March 26 2 / 23 Multi-attractor regime Result: to avoid multiple outcome (i.e. uncertainty in decision) speed up information dissemination (mass media,...) increase randomness in social interaction (T ) system globalized by ruling information becomes predictable to enhance multiple outcome (i.e. openess, diversity) increase self-confidence, local influences (s) prevent globalization via mass media (small D) locality matters system becomes unpredictable
21 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March / 23 Multi-attractor regime Communication on different time scales vary: d = D +1 /D 1 <x > t <x > t <x > t d=1.1 d=1.2 d=1.5 subpopulation with the more efficient communication becomes always the majority
22 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March / 23 Conclusions Conclusions Self-organization in distributed systems: based on the non-linear coupling of individual actions feedback mechanism: self-consistent field indirect communication, exchange of information non-equilibrium system: communication is costly generation of information requires energy self-organization: emergence of spatial patterns
23 Self-Organization and Collective Decision Making... Frank Schweitzer SYSS Dresden 31 March / 23 Conclusions Model of Brownian Agents: stochastic approach to structure formation in distributed systems ( micro level ) considers internal degrees of freedom and energetic conditions of agents gradual transition from physical to biological and social phenomena by adding complexity to the agents very flexible, versatile tool for investigating complex systems F.S., Brownian Agents and Active Particles. Collective Dynamics in the Natural and Social Sciences, Springer, 2nd ed. 24, 42 pp., 192 ill.
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