| Chaotic phenomena refer to a state of motion that is determined but unpredictable in nonlinear science.It is a complex phenomenon that appears to be irregular and inherently random in a deterministic system.The deterministic system refers to the chaotic system described by the determined dynamic equation;the randomness refers to the inherent randomness of chaos itself,and the system manifests itself as the unpredictability of long-term behavior.Due to the complexity of the chaotic system itself and the extreme sensitivity to the initial values,the study of chaotic system control is more challenging and practical.Based on the above background,this paper firstly introduces chaotic systems and complex network systems,including the origin,research status and classical control methods of chaos control and synchronization research.Then,an effective method is proposed to realize the functional projection synchronization of different dimensional complex chaotic systems with time-delay.A complex update rate of unknown parameters is designed to realize the synchronization between two complex chaotic systems.Finally,In order to synchronize the complex network system,an intermittent control scheme is proposed,and the exponential synchronization criterion of the complex network system is established.The control strategy of intermittent synchronization of complex network systems is obtained.This paper focuses on the following issues:1)The generalized complex modified mixed function projection synchronization(GCMHFPS)control problem for a class of time-delay chaotic(hyperchaotic)systems with unknown parameters is studied.Firstly,the synchronization error is defined by the complex function matrix,and a control method is proposed based on Lyapunov control principle.Secondly,the sufficient conditions of GCMHFPS in different dimensions are given to realize the GCMHFPS of complex systems with time delay.The estimation of the unknown complex parameter is given by adaptive law.Finally,the Matlab simulation of the complex Lü system and Lorenz system with time-delay is carried out to verify the effectiveness of the scheme.2)The problem of synchronous control for a class of network chaotic systems with time-delay is studied.Firstly,an exponential synchronization framework is established by the intermittent control scheme.In this scheme,the external coupling matrix is asymmetric or irreducible.Secondly,the control method is proposed for a class of networks with irreducible and balanced external coupling matrices by Lyapunov theorem.The synchronization is achieved by the intermittent control scheme.Finally,the Matlab simulation of Chen hyperchaotic network system is carried out to verify the correctness and feasibility of the scheme. |
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