Localized Turing and Turing-Hopf Patterns

Abstract

In systems driven away from thermodynamic equilibrium, patchiness often arises through the occurrence of symmetry breaking bifurcations. Diffusive instabilities resulting from differential diffusion processes acting in the presence of some autocatalytic kinetic scheme enter that class of phenomena to produce stationary space periodic (Turing) or spatiotemporal (Hopf) patterns. Turing patterns have at last recently been obtained when the isothermal Chlorite-Iodide-Malonic Acid (CIMA) reaction takes place in a continuously fed gel reactor in the presence of starch. On varying the malonic acid or starch concentrations a transition from stationary Turing structures to Hopf wavy patterns occurs. In the transition region, where both instabilities interact, a host of interesting behaviours may occur. Among these, new intrinsically localized patterns may form that give rise to new types of patchinesses. All of these structures may be accounted for through the study of the bifurcation behaviour of simple theoretical reaction-diffusion models.