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Competition in patchy environment with cross diffusion. (English) Zbl 1074.92033
Summary: We formulate a Lotka-Volterra competitive system in two patches in which the per capita migration rate of each species is influenced not only by its own but also by the other one’s density, i.e., there is cross diffusion present. Numerical studies show that at a critical value of the bifurcation parameter the system undergoes a Turing bifurcation and the cross-migration response is an important factor that should not be ignored when pattern emerges.

MSC:
92D40 Ecology
34C23 Bifurcation theory for ordinary differential equations
37N25 Dynamical systems in biology
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