American Institute of Mathematical Sciences

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July  2007, 8(1): 95-105. doi: 10.3934/dcdsb.2007.8.95

Interaction of diffusion and delay

Karl Peter Hadeler 1, and  Shigui Ruan 2,

1. 

School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, United States
2. 

Department of Mathematics, The University of Miami, P.O. Box 249085, Coral Gables, Florida 33124

Received  September 2006 Revised  November 2006 Published  April 2007

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 delay. But periodic oscillations, constant in space or with low spatial frequency, can be achieved via increasing the delay or changing the diffusion rates.
Keywords: matrix stability., time delay, Hopf bifurcation, Turing instability, Reaction-diffusion equations.
Mathematics Subject Classification: Primary: 92D25; Secondary: 35K5.
Citation: Karl Peter Hadeler, Shigui Ruan. Interaction of diffusion and delay. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 95-105. doi: 10.3934/dcdsb.2007.8.95
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