Mechanisms for stabilisation and destabilisation of systems of reaction-diffusion equations

S. A. Gourley, N. F. Britton, M. A J Chaplain, H. M. Byrne

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Potential mechanisms for stabilising and destabilising the spatially uniform steady states of systems of reaction-diffusion equations are examined. In the first instance the effect of introducing small periodic perturbations of the diffusion coefficients in a general system of reaction-diffusion equations is studied. Analytical results are proved for the case where the uniform steady state is marginally stable and demonstrate that the effect on the original system of such perturbations is one of stabilisation. Numerical simulations carried out on an ecological model of Levin and Segel (1976) confirm the analysis as well as extending it to the case where the perturbations are no longer small. Spatio-temporal delay is then introduced into the model. Analytical and numerical results are presented which show that the effect of the delay is to destabilise the original system.

Original languageEnglish
Pages (from-to)857-877
Number of pages21
JournalJournal of Mathematical Biology
Volume34
Issue number8
Publication statusPublished - 1996

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Reaction-diffusion Equations
Stabilization
Perturbation
diffusivity
Ecological Model
Diffusion Coefficient
Computer simulation
Numerical Simulation
Numerical Results
Demonstrate
Model

Keywords

  • Reaction-diffusion equations
  • Spatio-temporal delay
  • Time-periodic diffusion coefficients

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Mathematics (miscellaneous)

Cite this

Mechanisms for stabilisation and destabilisation of systems of reaction-diffusion equations. / Gourley, S. A.; Britton, N. F.; Chaplain, M. A J; Byrne, H. M.

In: Journal of Mathematical Biology, Vol. 34, No. 8, 1996, p. 857-877.

Research output: Contribution to journalArticle

Gourley, S. A. ; Britton, N. F. ; Chaplain, M. A J ; Byrne, H. M. / Mechanisms for stabilisation and destabilisation of systems of reaction-diffusion equations. In: Journal of Mathematical Biology. 1996 ; Vol. 34, No. 8. pp. 857-877.
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