In this paper, we give a quantitative estimate for the first N Lyapunov exponents random perturbations of natural class 2N-dimensional volume-preserving systems exhibiting strong hyperbolicity on large but noninvariant subset phase space. Concrete models covered by our setting include coupled standard maps, in both ‘weak’ and ‘strong’ coupling regimes.

In this paper we introduce the method for investigation of coupled chaotic systems using topological methods. We show that if the coupling is small then there exists independent symbolic dynamics for every coupled subsystem and in consequence the systems are not synchronized. As an example we consider coupled H enon maps. Using computer interval arithmetic we nd parameter mismatch and perturbat...

Cycling behavior involving steady-states and periodic solutions is known to be a generic feature of continuous dynamical systems with symmetry. Using Chua’s circuit equations and Lorenz equations, Dellnitz et al. [1995] showed that “cycling chaos”, in which solution trajectories cycle around symmetrically related chaotic sets, can also be found generically in coupled cell systems of differentia...