A Reactive System with Diffusive Transport Displaying Two Different Symmetry-Breaking Dissipative Structures

Abstract

An open reactive system is modelled by coupling the chemical kinetics to diffuse transport. This system operates far from the regime of linear irreversible thermodynamics. The kinetics correspond to a certain region in the parameter space of the Oregonator for which two symmetrybreakdowns occur: a) A periodic orbit contained in an unstable manifold of the phase space. This solution is invariant under time-translations generated by a period. b) A spatial stationary dissipative structure. This solution is invariant under a subgroup of the space symmetry group. The initial time periodicity of the system is followed by a spatial pattern. The restriction to the center manifold in the phase space allows to reduce an infinitedimensional problem for the bifurcation of a semiflow to a finite dimensional system of ordinary differential equations. The ranges in the control concentrations for this dynamics is found in accord with the experimental values. We also demonstrate that if the vessel is stirred after the Turing pattern has emerged, the freezed wave is destroyed and the time-periodic behavior is achieved again.