Coupled map model with a conserved order parameter

Abstract

The bifurcation structure and dynamics of a coupled map model with a conserved order parameter are studied. In a particular region of parameter space, the dynamics of the model mimics that of the continuum Cahn-Hilliard equation and gives rise to smooth, static structures. These structures are described in terms of the intersections of manifolds associated with the fixed points of a four-dimensional, conservative map, which is chaotic. The dimensionality of the map is a consequence of the conserved order parameter. In other regions of parameter space, the dynamics of the model gives rise to modulated structures with defects as well as various more complex spatio-temporal states.