Chaos and SelfOrganization in Satiotemporal Models of Ecology混沌和时空模型的自组织生态.pptVIP

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Chaos and SelfOrganization in Satiotemporal Models of Ecology混沌和时空模型的自组织生态.ppt

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Chaos and SelfOrganization in Satiotemporal Models of Ecology混沌和时空模型的自组织生态

Chaos and Self-Organization in Spatiotemporal Models of Ecology J. C. Sprott Department of Physics University of Wisconsin - Madison Presented at the Eighth International Symposium on Simulation Science in Hayama, Japan on March 5, 2003 Outline Historical forest data set Stochastic cellular automaton model Deterministic cellular automaton model Application to corrupted images Landscape of Early Southern Wisconsin (USA) Stochastic Cellular Automaton Model Cluster Probability A point is assumed to be part of a cluster if its 4 nearest neighbors are the same as it is. CP (Cluster probability) is the % of total points that are part of a cluster. Cluster Probabilities (1) Random initial conditions Cluster Probabilities (2) Ordered initial conditions Fluctuations in Cluster Probability Power Spectrum (2) No power law (1/fa) for r = 10 Simplified Model Previous model 6 levels of tree densities nonequal probabilities randomness in 3 places Simpler model 2 levels (binary) equal probabilities randomness in only 1 place Deterministic Cellular Automaton Model Why a deterministic model? Randomness conceals ignorance Simplicity can produce complexity Chaos requires determinism The rules provide insight Model Fitness Update Rules Genetic Algorithm Is it Self-organized Critical? Is it Chaotic? Conclusions Application to Corrupted Images Landscape with Missing Data Image with Corrupted Pixels Multispecies Lotka-Volterra Model with Evolution Multispecies Lotka-Volterra Model with Evolution Evolution of Total Biomass Conclusions Competitive exclusion eliminates most species. The dominant species is eventually killed and replaced by another. Evolution is punctuated rather than continual. Summary Nature is complex Simple models may suffice References Let Si(x,y) be density of the ith species (trees, rabbits, people, …) dSi / dt = riSi (1 - Si - Σ aijSj ) Choose ri and aij from a Poisson random distribution (both positive) Replace species that die with new ones