EVOLUTION OF PROBABILITY DENSITIES IN STOCHASTIC COUPLED SNAP LATTICES

This paper describes the statistical properties of coupled map lattice s subjected to the influence of stochastic perturbations. The stochast ic analog of the Perron-Frobenius operator is derived for various type s of noise. When the local dynamics satisfy rather mild conditions, th is equation is shown to possess either stable, steady state solutions (i.e., a stable invariant density) or density limit cycles. Convergenc e of the phase space densities to these limit cycle solutions explains the nonstationary behavior of statistical quantifiers at equilibrium. Numerical experiments performed on various lattices of tent, logistic , and shift maps with diffusivelike interelement couplings are examine d in light of these theoretical results.