Turing instabilities and patterns near a Hopf bifurcation

We derive a necessary and sufficient condition for Turing instabilities to occur in two-component systems of reaction-diffusion equations with Neumann boundary conditions. We apply this condition to reaction-diffusion systems built from vector fields with one fixed point and a supercritical Hopf bifurcation. For the Brusselator and the Ginzburg

• Type: Journal
• Year: 2005
• Where: AMC
• Authors: Rui Dilão
• Keywords: AMC 2005, Reaction-diffusion Equations, Turing, Two-component Systems