Generalized synchronization of chaos: The auxiliary system approach

Abstract

Synchronization of chaotic oscillators in a generalized sense leads to richer behavior than identical chaotic oscillations in coupled systems. It may imply a more complicated connection between the synchronized trajectories in the state spaces of coupled systems. We suggest a method here that can be used to detect and study generalized synchronization in drive-response systems. This technique, the auxiliary system method, utilizes a second, identical response system to monitor the synchronized motions. The method can be implemented both numerically and experimentally and in some cases it leads to analytical results for generalized synchronization.