Attractor and spatial chaos for the Brusselator in image Original Research Article

Brusselator is an important dynamical system which can be described by a reaction–diffusion system. In this paper it is proved that this reaction–diffusion system possesses a global attractor AA in the corresponding phase space. The upper and lower bounds of Kolmogorov εε-entropy of AA are obtained. Moreover we give a more detailed study of spatial chaos of the attractor AA for the Brusselator in RNRN. We interpret a group of spatial shifts as a dynamical system which acts on the attractor AA. By using the technique of unstable manifolds, it is proved that this dynamical system is chaotic. In order to clarify the nature of this chaos, we construct the Lipschitz-continuous homeomorphic embedding of a typical model dynamical system whose chaotic behavior is evident, into the spatial shifts on the attractor AA. This typical dynamical system generalizes the symbolic system. It was first introduced by Zelik.