Spatio-Temporal Chaos in Bistable Coupled Map Lattices

Abstract

In this chapter we consider lattice models with discrete time, i.e. dynamical systems with a discrete time, discrete space and continuous state and hence coupled map lattices (CML). CML describe the collective dynamics of a finite or infinite number of interacting finite-dimensional local dynamical systems (elements, units or cells) placed on the sites of a spatial lattice (the “physical” space). The dynamics of a single element is described by a point map. Thus, CML are characterized not only by their internal dynamics, i.e. that of the local elements, but also by the dynamics in the “physical” space. CML have been used to model a variety of phenomena including pattern formation, nonlinear waves, topological spatial chaos, distribution of defects in the spatial structures of nonlinear fields, reentry initiation in coupled parallel fibers, etc. [7.1–3, 7.6, 7.7, 7.9–16, 7.18, 7.20–22, 7.24, 7.25–31].