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Adaptive coupled synchronization among multi-Lorenz systems family. (English) Zbl 1143.93333

Summary: The adaptive synchronization method of coupled system is proposed for multi-Lorenz systems family. This method can avoid estimating the value of coupling coefficient. Strict theoretical proofs are given. And we derived a sufficient condition of synchronization for a general unidirectional coupling ring network with \(N\) identical Lorenz systems. The network is coupled through the first state variable of each equation. In fact, the whole unidirectional coupling network will be synchronized by adding only one adaptive feedback gain equation. Numerical simulations show the effectiveness of the methods.

MSC:

93D15 Stabilization of systems by feedback
34D20 Stability of solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
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