On the interaction of strange attractors

This paper deals with the dynamics of diffusively coupled strange attractors. Such interaction tends to equalize their instantaneous states and, for large coupling constant, results in a homogeneous state that is chaotic in time. The stability of this state depends on the relation between the Lyapunov exponent and the coupling constant. Statistical properties are determined for weakly inhomogeneous disturbances near a stable homogeneous regime. The inhomogeneous state beyond the stability threshold is treated by using the mean-field approximation. We show that both cases of soft (supercritical) and hard (subcritical) excitation of the inhomogeneous state may occur.