Differential flow induced transition of Hopf instability to Turing instability and pattern formation

Abstract

An external electric field may affect mass transport in a reaction-diffusion system. We show that a symmetry breaking instability leading to formation of spatial structures may result in when a constant external electric field normal to the reaction plane causes a diffusion-driven stable state (in absence of diffusion the steady state is homogeneous and unstable due to Hopf bifurcation) to become unstable. We trace its origin in an interesting transition of Hopf instability to reaction-diffusion instability triggered by a differential flow in presence of electric field. We carry out a numerical simulation in three dimensions on a chemical system (chlorite-iodide-malonic acid). The pattern is generically different from the electric field deformed Turing pattern.