Abstract
We study the effect of the network structure on the dynamic stability in the diffusively coupled Lotka–Volterra system. Here we present a metapopulation model for the Lotka–Volterra system on various graphs. The total population is assumed to consist of several subpopulations (nodes). Each individual migrates by random walk; the destination of migration is randomly determined. From reaction–diffusion equations, we obtain the population dynamics. The numerical analyses are performed only for a few and characteristic values of the parameters representing typical behaviors. It is found that the dynamics highly depends on network structures. When a network is homogeneous, the dynamics are neutrally stable: each node has a periodic solution with neutral stability, and the oscillations synchronize in all nodes. However, when a network is heterogeneous, the dynamics approach stable focus and all nodes reach equilibriums with different densities. Hence, the heterogeneity of the network induces dynamic stabilization.
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