Bifurcations and turing instabilities in reaction-difussion systems with time-dependent dissusivities

Abstract

A class of two-component,one-dimensional, reaction-diffusion systems of the type usually found in Ecology are analysed in order to establish the qualitative behaviour of solutions. It is shown that for diffusivities in the form Dj = dj + bjcos(wt + ), relationships can be derived from which amplitude destabilisation can be assessed dep ending on the wavenumber k and the variable diffusion coefficients, specially the frequency w. Therefore time-dependent diffusivities can control the Turing instability mechanism. The analysis is performed using F loquet's Theory. Numerical simulations for various kinetics are presented, and bifurcation diagrams in the plane (k,w) are obtained.