Spatial pattern formation of prey-predator populations
SummaryFormation of a non-uniform spatial distribution pattern of prey and predator populations in a heterogeneous environment is mathematically investigated. Both populations are distributed in linearly connected compartments. Furthermore it is assumed that only the predator species (animal) can randomly diffuse across the boundaries but the prey species (plant) are confined in each compartment. When the prey-predator relation is given by a simple Volterra type interaction it is known that the system cannot establish a non-uniform stationary distribution in a homogeneous environment. However, in a heterogeneous environment, it can be analytically shown by constructing a Lyapunov function that the system asymptotically and globally tends to a non-uniform stationary distribution. Thus, the populations are stabilized by the heterogeneity of environment.