Thursday, August 9, 2007 - 10:30 AM

COS 116-8: Chaotic dynamics lost in small-world network meta-populations

Colin T. Kremer, Chris C Leary, Gary W Towsley, and Gregg Hartvigsen. State University of New York College at Geneseo

Chaotic population dynamics predicted by mathematical models are rarely observed in empirical systems. This may arise from moderating interactions, such as the dispersal of organisms in space, occurring within empirical systems that are not captured by current models. Another possibility is that the observation of chaotic dynamics may depend on the scale at which empirical systems are studied. To study the influence of these factors on chaotic population dynamics, we construct a metapopulation model composed of subpopulations governed independently by the logistic growth equation under chaotic conditions. Subpopulations are connected on a small-world network, rather than a more traditional lattice structure. We test both density dependent and independent dispersal between subpopulations on this network. Additionally, we consider the effects of varying dispersal level and network structure. We present a method for estimating the maximum Lyapunov exponent, which is used to determine the level of chaotic behavior in this complex system. We find that a metapopulation’s dynamics remain chaotic independent of an increase in the number of subpopulations. Under high levels of dispersal on random graphs, non-chaotic metapopulation dynamics are observed. We found no significant difference between dispersal types. These results suggest that the dispersal of organisms in space within empirical systems can moderate underlying chaotic dynamics, possibly accounting for discrepancies between theoretical and empirical dynamics.

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