MECHANISMS FOR STABILIZATION AND DESTABILIZATION OF SYSTEMS OF REACTION-DIFFUSION EQUATIONS

Potential mechanisms for stabilising and destabilising the spatially u niform steady states of systems of reaction-diffusion equations are ex amined. In the first instance the effect of introducing small periodic perturbations of the diffusion coefficients in a general system of re action-diffusion equations is studied. Analytical results are proved f or the case where the uniform steady state is marginally stable and de monstrate that the effect on the original system of such perturbations is one of stabilisation. Numerical simulations carried out on an ecol ogical 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 a nd numerical results are presented which show that the effect of the d elay is to destabilise the original system.