Turing bifurcation in a human migration model of scheurle-seydel type

摘要

The main goal of this paper is to continue the investigations of the important system proposed by [Scheurle & Seydel, 2000] and modified by [Sándor, 2003]. I consider spatio-temporal models for the behavior of students in graduate programs at neighboring universities as systems of ODE which describe two-identical patch-two-species systems linked by migration, where the phenomenon of the Turing bifurcation occurs. It is assumed in the model that the per capita migration rate of each individual is influenced not only by its own (Fickian) but also by the other densities, i.e. there is cross diffusion present. We study the conditions of the existence and stability properties of the equilibrium solutions in a kinetic model (no migration). We will show that analytically at a critical value of a parameter a Turing bifurcation takes place: a spatially nonhomogenous solution (pattern) arises. A numerical example is also included.