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Zbl 1128.92001
Hadeler, Karl P.; Ruan, Shigui
Interaction of diffusion and delay. (English)
[J] Discrete Contin. Dyn. Syst., Ser. B 8, No. 1, 95-105 (2007). ISSN 1531-3492; ISSN 1553-524X/e

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 2000:: *92B05 General biology and biomathematics
34K60 Applications of functional-differential equations
35K57 Reaction-diffusion equations
92D25 Population dynamics

Keywords: time delay; Hopf bifurcation; matrix stability; predator-prey model

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