Generalizations of the concept of marginal synchronization of chaos

Generalizations of the concept of marginal synchronization between chaotic systems, i.e. synchronization with zero largest conditional Lyapunov expone nt, are considered. Generalized marginal synchronization in drive-response systems is defined, for which the function between points of attractors of different systems is given up to a constant. Auxiliary, system approach is shown to be able to detect this synchronization. Marginal synchronization i n mutually coupled systems which can be viewed as drive-response systems wi th the response system influencing the drive system dynamics is also consid ered, and an example from solid-state physics is analyzed. Stability of the se kinds of synchronization against changes of system parameters and noise is investigated. In drive-response systems generalized marginal synchroniza tion is shown to be rather sensitive to the changes of parameters and may d isappear either due to the loss of stability of the response system, or as a result of the blowout bifurcation. Nonlinear coupling of the drive system to the response system can stabilize marginal synchronization. (C) 2000 El sevier Science Ltd. All rights reserved.