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Adaptive synchronization of two novel different hyperchaotic systems with partly uncertain parameters. (English) Zbl 1182.37028

Chaos synchronization plays an important role for understanding the cooperative behavior in coupled chaotic oscillators.

A variety of approaches have been proposed for the synchronization of chaotic and hyperchaotic systems such as linear and nonlinear feedback synchronization methods, adaptive synchronization methods, backstepping design methods, and sliding mode control methods etc. However, most of the methods mentioned above and many other existing synchronization methods mainly concern the synchronization of two identical chaotic or hyperchaotic systems, the methods of synchronization of two different chaotic or hyperchaotic systems are far from being straight-forward because of their different structures and parameter mismatch.

This paper addresses the problem of adaptive synchronization of two different new hyperchaotic systems with some uncertain parameters. On the basis of the Lyapunov stability theory and the adaptive control theory, a new adaptive synchronization control law and a novel parameter estimation update law are proposed to achieve synchronization between the two novel different hyperchaotic systems with uncertain parameters. Numerical simulations are given to demonstrate the effectiveness of the proposed synchronization scheme and verify the theoretical results.

MSC:
37D45Strange attractors, chaotic dynamics
93C40Adaptive control systems
37B25Lyapunov functions and stability; attractors, repellers
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