Migration difference in diffusively-coupled prey–predator system on heterogeneous graphs

Abstract

When the migration rate of predators is definitely different from that of prey, the metapopulation dynamics on heterogeneous graphs change greatly with migration rate. We study the effect of the migration difference on the metapopulation dynamics in the diffusively coupled prey–predator system on homogeneous and heterogeneous graphs. We present a metapopulation model on various graphs for the prey–predator system with different migration rates. The total population is assumed to consist of several subpopulations (patches or nodes). Each individual migrates by random walk; the destination of migration is randomly determined. The migration rates of prey and predators are represented by different diffusion constants. From reaction–diffusion equations with two different diffusion constants, we obtain the population dynamics. The numerical analyzes are performed only for a few and characteristic values of the parameters representing typical behaviors. When a network is homogeneous, the dynamics are neutrally stable and the equilibrium point does not depend on diffusion constants. However, when a network is heterogeneous, the dynamics approach stable focus and the equilibrium values of prey’s and predator’s numbers vary with two diffusion constants. It is found that the metapopulation dynamics on heterogeneous graphs depend highly on two diffusion constants of prey and predators.