Synchronization Research Of Several Kinds Of Complex Dynamic Systems

Complex dynamic systems exist widely in nature and human society.The study of complex dynamic systems has great significance to the development of science and society.Synchronization is one of the dynamic behaviors of complex dynamic systems.With the in-depth study of complex dynamic systems,the synchronization research of complex systems has been widely used in mathematics,biomedicine,artificial intelligence,automation and other disciplines.Based on the idea of impulse control,nonlinear control theory and Lyapunov stability theory,this article analyzes the synchronous control problems of several types of complex dynamic systems.The main research contents are as follows:(1)Dual-channel combined function projection synchronization of multiple chaotic drive-response systems is researched.A dual-channel synchronous system is established,in which each channel contains two chaotic drive systems and a chaotic response system.In order to overcome the influence of external disturbance and unknown parameters,a robust adaptive controller and corresponding parameter adaptive laws are designed.The combined synchronization of dual-channel drive-response chaotic systems under the corresponding function scale factor matrix is realized.(2)The synchronization time of chaotic systems is further discussed.The chaotic system model with external disturbance is established.Based on the finite-time and fixed-time synchronization theory,the sufficient conditions for the finite-time and fixed-time synchronization of chaotic systems are given.Based on Lyapunov stability theorem and inequality transformation,finite-time synchronization and fixed-time synchronization controllers are designed,respectively.In the numerical simulation,the finite-time and fixed-time combined synchronization of the three-dimensional chaotic system and the four-dimensional hyperchaotic system are realized by the designed controller.(3)The complete synchronization of coupled neural networks is studied.Considering the possible time-delay in system operation,a time-delay neural network model with N nodes is constructed.Based on the impulse inequality convergence criterion,a distributed delayed impulse controller is designed to realize the complete synchronization of the neural network.The parameter matrix and gain matrix in the neural network are obtained by MATLAB LMI tool.The simulation experiment proves the feasibility of the theoretical results.(4)On the basis of the synchronization research of time-delay coupled neural network,a discontinuous output coupled neural network model with impulsive effect is constructed.Through the designed fixed time synchronization controller,the fixed-time output synchronization of coupled neural networks is realized.In the output synchronization,the dimension of the output state vector can be different from the dimension of the input state vector,that is,it is not necessary for all states to be synchronized.Compared with finite-time synchronization,the synchronization time of fixed-time synchronization is not affected by the initial conditions of the system.