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We investigate the synchronization of chaotic oscillations in coupled oscillator systems, both theoretically and in analog electronic circuits. Particular attention is paid to deriving and testing general conditions for the stability of synchronous chaotic behavior in cases where the coupled oscillator array possesses a shift-invariant symmetry. These cases include the well studied cases of nearest-neighbor diffusive coupling and all-to-all or global coupling. An approximate criterion is developed to predict the stability of synchronous chaotic oscillations in the strong coupling limit, when the oscillators are coupled through a single coordinate (scalar coupling). This stability criterion is illustrated numerically in a set of coupled R\"ossler-like oscillators. Synchronization experiments with coupled R\"ossler-like oscillator circuits are also carried out to demonstrate the applicability of the theory to real systems.
Heagy et al. (Thu,) studied this question.