Partial synchronization in coupled chemical chaotic oscillators. (English) Zbl 1194.34095

Synchronized dynamics is studied in systems of diffusively coupled chaotic Rössler-like oscillators which could be derived from a chemical reaction. It is shown that for the coupled oscillators the global asymptotic stability of the complete synchronization cannot be achieved since two fixed points exist outside of the synchronization manifold. However, for a system of three coupled oscillators a regime of partial synchronization, where only two oscillators synchronize, is argued to be globally asymptotically stable if the coupling strength among oscillators is large enough. The corresponding sufficient condition for the coupling strength is obtained. Theoretical analysis is supported by numerical simulations which illustrate synchronized and desynchronized dynamics.


34D06 Synchronization of solutions to ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
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