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Interaction of diffusion and delay. (English) Zbl 1128.92001
Summary: For reaction-diffusion equations with delay, the joint effects of diffusion and delay are studied. In particular, for two-dimensional systems where only the interaction between species is delayed, the interdependence of stability against delay and against diffusion (Turing instability) can be clearly exhibited. Turing instabilities occur largely independent of delays. But periodic oscillations, constant in space or with low spatial frequency, can be achieved via increasing the delay or changing the diffusion rates.
MSC:
92B05General biology and biomathematics
34K60Qualitative investigation and simulation of models
35K57Reaction-diffusion equations
92D25Population dynamics (general)