Design Of Memristor-based Chaotic System And Research On Complex Multistability

In recent decades,with the continuous deep study of chaotic theory,exploring novel chaotic systems with complex dynamic behavior has become a popular direction in the field.As an important aspect of nonlinear dynamics,the coexistence and multistability of chaotic attractors have attracted widespread attention from scholars at home and abroad.Generally speaking,nonlinear systems with multistability are often accompanied by more complex dynamic behaviors,and the chaotic signals or sequences generated by them will also show stronger pseudo-randomness and unpredictability,which is of great significance to the research of information security and other fields.There are extensive memory effects in nature and human society,and the memristor,as a new circuit element with typical memory function,not only fills the gap in the relationship between charge and flux,but also makes the connection between basic variables in circuit theory more complete.With its unique nonlinear advantages,memristor has been widely used in nonlinear chaotic systems,combinatorial logic circuits and memristor neural networks.In this paper,we will study the application of memristors in chaotic systems,and deeply explore the basic dynamics and multistability of the improved system.The main contents of the paper are as follows:(1)Symmetric coexistence attractor is a special kind of multistable phenomenon.A simple three-dimensional chaotic system is designed by introducing two linear terms into the classical Liu-Chen system.Then,the physical phenomena of symmetric coexistence attractor,asymmetric coexistence attractor and transient coexistence attractor of the system are studied.Finally,the circuit design and simulation of the system are completed,and the chaotic attractors of four and single vortex are observed.(2)A five-valued piecewise memristor model is constructed.By analyzing the voltammetry of the model,it is found that the model has a typical tight hysteresis loop,which is consistent with the essential characteristics of the memristor.Subsequently,a five-value memristor chaotic system is proposed based on this model and found that in addition to the general chaotic properties,it has special phenomena such as hidden multistability,super multistability,and transient chaos.Finally,the complexity of the new system is proved by circuit simulation.(3)A four-dimensional Jerk hyperchaotic system based on cubic continuous memristor is designed in this paper.The system has multiple alternating behaviors among periodic,chaotic and hyperchaotic,and the displacement of chaotic attractor occurs under the control of offset constant.Then,the multistability of the system is analyzed,a variety of asymmetric coexistence attractors are found,and their symmetric coexistence attractors are explained combined with the attraction basin.Finally,the circuit design and simulation are completed according to the dimensionless system equation to verify the theoretical analysis.