Research On Chaotic Characteristics Of Nonlinear Systems With Hidden Attractors

There are a lot of nonlinear phenomena in the real world,which will lead to chaos under certain conditions.Although chaos appears irregular characteristics on the surface,people gradually find that it also hides the essential characteristics of order.In 1994,J.C.Sprott constructed nineteen kinds of systems with quadratic nonlinear terms and found a large number of chaotic phenomena.In recent years,many people improve it and get rich results,including scroll hidden attractors.Chaotic systems with multi-scroll hidden attractors are much more complex than chaotic systems with only a few attractors,which play an important role in chaotic communication security research,chaotic cryptography analysis and image encryption applications.Therefore,the generation,control and synchronization of multi-scroll hidden attractors have attracted the attention of many researchers.In this paper,the dynamics of two nonlinear chaotic systems are analyzed and the multi-roll hidden attractor is obtained.Firstly,the sine function is used as a nonlinear term to introduce the Jerk system with equilibrium points.The phase orbits of the system in different time units are obtained through numerical simulation,and the motion state of the system and the motion characteristics of the multi-scroll attractors are analyzed.Then,by adjusting the parameter b in the sine function,the phase orbits of the system in different time units are obtained,and the parameter characteristics of the system’s multi-scroll attractor are summarized.Then,according to the Jerk system with sine function,the corresponding circuit is designed,and the generated voltage waveform is compared with the corresponding phase orbits,which verify the correctness of the conclusion.It lays a good foundation for the further study of the system.If there is an equilibrium point in the system,it will be of great help for us to induce the generation of chaotic attractors and to control the chaos to a desired equilibrium state through certain methods.However,for a system with non-equilibrium point,the difficulty of generating and controlling chaotic attractors will be greatly increased because there is no equilibrium point in the system.Therefore,in order to study the induction method and motion characteristics of chaotic attractors for nonlinear systems without equilibrium point,we select the improved Sprott-A system without equilibrium point,and introduce the sine function containing parameters into the system.Through numerical simulation,the phase orbits under different time units,time evolution and bifurcation diagram of the system are obtained.The dynamic characteristics of the system under chaotic state,the motion characteristics of the multi-scroll hidden attractor,and the influence of the parameters on the motion state of the system and the changes of the scroll hidden attractor are analyzed.Furthermore,the simulation circuit of the system is designed,while the system is initially circuitalized,the results of circuit simulation and numerical simulation are compared to verify the correctness of the conclusion.It lays a great foundation for the practical application of the system.Through the study of nonlinear chaotic systems with multi-scroll hidden attractors,it can be obtained that the sine function can be properly introduced into a nonlinear systems without equilibrium point to obtain multi-scroll hidden attractors.And because the sine function can be obtained easily in the actual circuit,the difficulty to realize the application is greatly reduced,which has important research significance in the practical application.At the same time,how to construct multi-scroll hidden attractors in the new chaotic system will get more research.