Diffusion-driven destabilization of spatially homogeneous limit cycles in reaction-diffusion systems

Diffusion-Driven Instability in Reaction Diffusion Systems

For a stable matrix A with real entries, sufficient and necessary conditions for A D to be stable for all non-negative diagonal matrices D are obtained. Implications of these conditions for the stability and instability of constant steadystate solutions to reaction diffusion systems are discussed and an example is given to show applications. 2001 Academic Press

Homogeneous Reaction Diffusion

1. Electrocatalysis: This is one of the direct examples of the homogeneous reaction diffusion regime. This involves multiple steps, i.e. diffusion, adsorption and a possible charge transfer at the surface (x = 0). As shown in the schematic of Fig(1), species will adsorb on the catalyst surface, then diffuse along the surface to the right/left surfaces where a charge transfer reaction can occur....

Traveling avalanche waves in spatially discrete bistable reaction–diffusion systems

Infinitely extended two-dimensional reaction–diffusion lattices composed of bistable cells are considered. A class of particular stable stationary solutions, called pattern solutions, is introduced and examples are given. Pattern solutions persist at high diffusion coefficients whereas all other stable stationary solutions, with the exception of the constant solutions, disappear one after the o...

Pattern formation in reaction-diffusion and reaction-diffusion-convection systems

Canards and Bifurcation Delays of Spatially Homogeneous and Inhomogeneous Types in Reaction-diffusion Equations

In ordinary differential equations of singular perturbation type, the dynamics of solutions near saddle-node bifurcations of equilibria are rich. Canard solutions can arise, which, after spending time near an attracting equilibrium, stay near a repelling branch of equilibria for long intervals of time before finally returning to a neighborhood of the attracting equilibrium (or of another attrac...