Synchronized states in chaotic systems coupled indirectly through a dynamic environment.

We consider synchronization of chaotic systems coupled indirectly through common environment where the environment has an intrinsic dynamics of its own modulated via feedback from the systems. We find that a rich variety of synchronization behavior, such as in-phase, antiphase, complete, and antisynchronization, is possible. We present an approximate stability analysis for the different synchronization behaviors. The transitions to different states of synchronous behavior are analyzed in the parameter plane of coupling strengths by numerical studies for specific cases such as Rössler and Lorenz systems and are characterized using various indices such as correlation, average phase difference, and Lyapunov exponents. The threshold condition obtained from numerical analysis is found to agree with that from the stability analysis.