Spatially inhomogeneous modes of logistic differential equation with delay and small diffusion in a flat area

Abstract

In the paper we consider the problem of searching for coexisting modes in a nonlinear boundary value problem with a delay from population dynamics. For this we construct the asymptotic of spatially homogeneous cycle using the normal forms method and research the dependence of its stability on the diffusion parameter. Then we find coexisting attractors of the problem using numerical methods. Numerical experiment required an application of massively parallel computing systems and adaptation of solutions search algorithms to them. Based on the numerical analysis we come to the conclusion of the existence in the boundary value problem of solutions of two types. The first type has a simple spatial distribution and inherits the properties of a homogeneous solution. The second called the mode of self-organization is more complex distributed in space and is much more preferred in terms of population dynamics.