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Adaptive synchronization of coupled chaotic delayed systems based on parameter identification and its applications. (English) Zbl 1142.34387
Summary: This paper investigates the synchronization dynamics of a large class of chaotic delayed systems with all the parameters unknown. By a simple combination of adaptive control and linear feedback with the updating laws, some simple yet generic criteria for determining global synchronization based on parameter identification of uncertain chaotic delayed systems are derived by using the invariance principle of functional differential equations. It is shown that the approaches developed here further extend the ideas and techniques presented in recent literature. Furthermore, the theoretical results are applied to the well-known Chua’s circuit and a typical class of chaotic delayed Hopfield neural networks. Numerical simulations also demonstrate the effectiveness and feasibility of the proposed techniques.
MSC:
34K25Asymptotic theory of functional-differential equations
93D15Stabilization of systems by feedback
93D21Adaptive or robust stabilization
34K23Complex (chaotic) behavior of solutions of functional-differential equations
92B20General theory of neural networks (mathematical biology)
34K23Complex (chaotic) behavior of solutions of functional-differential equations