Interaction of diffusion and delay

Karl P. Hadeler, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)95-105
Number of pages11
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number1
StatePublished - Jul 1 2007


  • Hopf bifurcation
  • Matrix stability
  • Reaction-diffusion equations
  • Time delay
  • Turing instability

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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