Synchronization of identical neural networks and other systems with an adaptive coupling strength

In this paper, a new scheme to synchronize linearly or nonlinearly coupled identical circuit systems, which include neural networks and other systems, with an adaptive coupling strength is proposed. Unlike other adaptive schemes that synchronize coupled circuit systems to a specified trajectory (or an equilibrium point) of the uncoupled node by adding negative feedbacks adaptively, here the new adaptive scheme for the coupling strength is used to synchronize coupled systems without knowing the final synchronization trajectory. Moreover, the adaptive scheme is applicable when the coupling matrix is unknown or time-varying. The validity of the new adaptive scheme is also proved rigorously. Finally, several numerical simulations to synchronize coupled neural networks, Chua's circuits and Lorenz systems, are also given to show the effectiveness of the theory. Copyright (C) 2009 John Wiley & Sons, Ltd.