Chaotic Dynamics And Synchronization Of A Class Of Fractional Complex-valued Systems

In recent years,with the wide application of fractional calculus in image processing,signal processing and neural networks,it has attracted wide attention of scholars at home and abroad,and has simulated research on its dynamical analysis and practical applications.On the other hand,complex-valued systems can solve many problems that real-valued systems can not solve because of its wider coverage and closer to reality in nature.Therefore,studying the dynamical behavior of fractional complex-valued systems,including stability,chaos,control and synchronization,has not only theoretical significance,but also practical application value.The thesis mainly explores the chaotic dynamic behavior and synchronization control of a class of complex-valued fractional-order systems.Through theoretical analysis,the design method of the controller to ensure the synchronization of the system is obtained.The system model is simulated by Matlab mathematical tools,which proves the correctness of mathematical analysis and control methods.This thesis is divided into six chapters and arranged as follows:The first chapter introduces the research background and current situation of complex fractional-order system,as well as the concept,numerical method for fractional calculus,and the main content of this thesis.In the second chapter,the chaotic dynamics and chaotic control of complex-valued fractional-order Chen system are studied.Firstly,by using numerical simulation,the chaotic characteristics of the studied system are analyzed,and the fractional order to guarantee chaotic attractors is determined.Then,the control of fractional-order complex-valued chaotic system is realized by designing the controller,and the theoretical proof is given.The simulation examples also verifies the effectiveness of the designed controller.In the third chapter,the synchronization and control of complex-valued Chen systems with the same fractional order and structure are studied.Based on fractional Lyapunov function method,two kinds of appropriate feedback controllers are designed by using the eigenvalues of the system matrix and the matrices configuration method to realize the synchronization of the fractional-order chaotic complex-valued systems.The predictor-corrector algorithm is used in the simulation.The experimental results show that the designed control methods are effective.In the fourth chapter,the synchronization problems of fractional-order complex-valued systems with different order are studied.Two nonlinear feedback controllers are designed.The synchronization problem of the complex-valued Chen system with different fractional-order is transformed into the synchronization of the complex-valued Chen system with identical fractional.Based on fractional Lyapunov function,generalized projection synchronization and generalized dislocation projection synchronization,are discussed.The design method is verified by experimental simulations.In the fifth chapter,the control of fractional-order complex-valued chaotic dynamical systems with time-delay and synchronization of different fractional-order complex-valued chaotic dynamical systems with time-delay are studied.two kinds of feedback controllers are proposed to control and synchronize the delayed fractional-order complex-valued Chen systems.The experimental results in Matlab show that the selected controller is feasible.In the sixth chapter,the main work of this thesis are summarized,and makes further expectation for future work.