Asymptotic stability of densities in coupled map lattices (original) (raw)

Sufficient conditions for the asymptotic stability (strong convergence) of density evolution in finite dimensional piecewise monotone map lattices with both constant and state dependent coupling are given. These conditions are quite useful in numerical work since they allow one to precisely define where one expects to see numerical signatures of asymptotic stability. Asymptotic stability is illustrated with several examples. It is also shown that in constantly coupled lattices the density formed by collapsing the higher dimensional density into one dimension can be approximated by the evolution of densities under the action of an appropriately perturbed one-dimensional map.