Study On Synchronization Control Of Hybrid-Order Complex Lorenz Chaotic System

Chaos has become a research hotspot in the field of nonlinear science because of its rich dynamic behavior.Since the complex Lorenz chaotic system was proposed,people have found that complex variables can produce more complex dynamic characteristics and have broader application prospects.Therefore,this thesis first analyzes the method of steady-state control of complex chaotic systems and proposes a hybrid-order complex Lorenz system.The chaotic characteristics and special attractors are analyzed,and the concept of order attractor is proposed.The steady-state control and synchronization control of the hybrid-order complex Lorenz system are realized.The main contents and innovations are as follows:(1)Steady-state control of complex chaotic systemsFor the integer-order complex chaotic system,the principle and method of steadystate control of chaotic attractors are studied.Two controllers are proposed to make the chaotic system obtain steady-state attractors with predetermined position and expected shape.Finally,the effectiveness of the steady-state control of integer-order complex Lorenz chaotic system,integer-order complex Chen chaotic system and an actual physical model Duffing oscillator is verified by numerical simulation.(2)Analysis of chaotic characteristics of hybrid-order complex Lorenz systemsFirst,combining the advantages of both integer-order and fractional-order complex chaotic systems,a class of hybrid order complex Lorenz systems is proposed,and its system characteristics are analyzed.We demonstrate its abundant chaotic characteristics,including symmetry and dissipation,fixed points,and their stability and Lyapunov exponents,with “0-1” test.Second,when the initial value,parameters,and the order are varying,the system exhibits different dynamic behaviors,including fixed points,limit cycles,and chaotic attractors.It is further proved that the system has coexisting attractors and parametric attractors.In addition,we find that the system generates different chaotic attractors as the system hybrid order varies,referred to as order attractors.The concept of order attractors is proposed.(3)Dynamic transport of hybrid-order complex Lorenz systemFirst,the dynamic transport principle of hybrid-order complex Lorenz system is studied and design a piecewise continuous controller to realize offset boosting control.Second,two types of dynamic transport are achieved using a offset boosting control.One is dynamic transport in the state variable dimension,and the other is dynamic transport in the space of initial values,parameters or orders.By varying the initial value,parameters or orders,we realize the dynamic transport of the system.Finally,our simulation results confirm the dynamic transport of the hybrid-order complex Lorenz system.(4)Synchronization control of hybrid-order complex Lorenz systemDesign an anti-synchronization controller for hybrid-order complex chaotic systems.First,the anti-synchronization method of general hybrid-order chaotic systems is proposed.Second,the finite-time anti-synchronization control method of hybrid-order chaotic systems is proposed by using the finite-time synchronization theory.Finally,the effectiveness of the control method is proved mathematically,and simulation experiments were conducted on a hybrid-order complex Lorenz chaotic system to verify the effectiveness of the controller.