Interaction of diffusion and delay

Karl Peter Hadeler; Shigui Ruan

doi:10.3934/dcdsb.2007.8.95

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2007, Volume 8, Issue 1: 95-105. Doi: 10.3934/dcdsb.2007.8.95

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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
2.
Department of Mathematics, The University of Miami, P.O. Box 249085, Coral Gables, Florida 33124

Received: August 31, 2006

Revised: October 31, 2006

Published: December 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 92D25; Secondary: 35K57.

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