Analysis And Control Of Memristor Chaotic System With Multiple Coexisting Attractors

As a non-linear storage element,it can be widely used in many fields,such as resistance volt ampere effect and capacitance hysteresis effect.Multiple stability depending on the initial value,that is,multiple coexisting attractors,refers to the coexistence of multiple attractors(or equilibrium states)of a fixed parameter set.It plays an important role in the study of chaotic dynamics of many nonlinear systems.Because the system contains multiple coexisting attractors,with the change of the starting conditions of the nonlinear system,the trajectory will selectively converge to different states according to the different starting conditions.When the system contains an infinite number of coexisting attractors,the "extreme multi stability" will be used to describe this very special phenomenon.In order to make the system adapt to a variety of different working scenarios,appropriate control is applied to the system to make the system switch freely between two or more different states.Therefore,in recent years,coexistence attractors have attracted more and more attention.Firstly,a memristor chaotic system with a finite number of coexisting attractors is proposed.The dynamic behavior of the system is analyzed.The simulation circuit is built and the simulation test of the proposed system is carried out.In addition,the synchronization control of the system is also studied.According to the above research,it can be seen that the trajectory of the system will be affected not only by the system parameters,but also by the starting conditions.Therefore,the system can produce the coexistence phenomena of single scroll chaotic attractor and double scroll chaotic attractor,periodic coexistence,coexistence chaotic attractor and bifurcation coexistence.In addition,the system is simulated by circuit simulation,and the results are consistent with the theoretical analysis,so as to determine the feasibility of the scheme.Based on the existing theory,a controller suitable for the system is proposed.The adaptive synchronization is realized on the premise of unknown system parameters.At the same time,the unknown parameters in the system can be identified.The effectiveness of the scheme is proved by simulation experiments.In addition,a memristor resistive chaotic system with infinite hidden attractors is also envisaged and realized.According to the dissipation characteristics,equilibrium point and stability,Lyapunov exponent and phase diagram,the complex dynamic behavior changing with various parameters and initial states in the system is studied,and the numerical simulation results are used to determine various conditions in the system with the changes of parameters and initial states,such as periodic coexistence,quasi periodic coexistence The coexistence of chaotic attractors or the coexistence of infinite attractors.Combined with the characteristics of Lyapunov exponent of the system,the linear feedback control scheme is used to study the synchronization of the system.