Synchronization of chaos using proportional feedback

Synchronization of chaotic systems: Transverse stability of trajectories in invariant manifolds

We examine synchronization of identical chaotic systems coupled in a drive/response manner. A rigorous criterion is presented which, if satisfied, guarantees that synchronization to the driving trajectory is linearly stable to perturbations. An easy to use approximate criterion for estimating linear stability is also presented. One major advantage of these criteria is that, for simple systems, many of the calculations needed to implement them can be performed analytically. Geometrical interpretations of the criterion are discussed, as well as how they may be used to investigate synchronization between mutual coupled systems and the stability of invariant manifolds within a dynamical system. Finally, the relationship between our criterion and results from control theory are discussed. Analytical and numerical results from tests of these criteria on four different dynamical systems are presented. (c) 1997 American Institute of Physics.

Master-slave synchronization from the point of view of global dynamics

We present a mathematical framework for the theory of a synchronization phenomenon for dynamical systems discovered by Pecora and Carroll [Phys. Rev. Lett. 64, 821-824 (1990)]. From this perspective, we can synchronize, using a single coordinate, an open dense set of linear systems. We use our insights to synchronize nonlinear systems which were not previously recognized as being synchronizable. (c) 1995 American Institute of Physics.