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Synchronizing chaotic systems using control based on a special matrix structure and extending to fractional chaotic systems. (English) Zbl 1221.37212

Summary: We present a direct approach to design a stabilizing controller based on a special matrix structure to synchronize chaotic systems and extends the approach to synchronize fractional chaotic systems. With this method, chaos synchronization is implemented in Lorenz chaotic systems with known parameters and the same to Lorenz chaotic systems with unknown parameters. Especially, fractional Lorenz chaotic system with unknown parameters is synchronized by fractional Chen chaotic system, too. Numerical simulations confirm the effectiveness of the method proposed.

MSC:

37N35 Dynamical systems in control
34H10 Chaos control for problems involving ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
34D06 Synchronization of solutions to ordinary differential equations
93D21 Adaptive or robust stabilization
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