Bifurcations and turing instabilities in reaction-diffusion systems with time-dependent diffusivities

Abstract

A class of two-component, one-diemnsional, react-diffusion systems of the type usually found in Ecology are analysed in order to establish the qualitative behavior of solutions. It is shown that for diffusivities in the form D_j=d_j+b_j cos⁡(ωt+ ϕ) relationships can be derived from which amplitude destabilization can be assessed depending on the wavenumber k and the variable diffusion coefficients, specially the frequency ω. Therefore, time-dependent diffusivities can control the turing instability mechanism. The analysis is perfirmed using Floquet´s Theory. Numerical simulations for various kinetics are presented, and bifurcation diagrams in the plane (k, ω) are obtained