Research On New Hyper-chaotic System With Coexistence Attractors And Its Control

With the continuous development of chaos theory,hyper-chaotic systems without equilibrium points have gradually become one of the research hotspots in the nonlinear field because of hidden attractors.Fractional order can more accurately describe the nature of nonlinear chaotic systems and things.Therefore,fractional order systems without equilibrium points have more research value.Systems without equilibrium points have symmetry and asymmetric coexistence attractors.Asymmetric coexistence attractors are more complicated in position and type than symmetric coexistence attractors.Offset boosting also makes the attractor become another attractor along the boundary of the attraction domain,resulting in coexistence phenomenon.Hyper-chaotic systems with different types of coexistence attractors have multi-stability and extreme multi-stability,which will affect engineering to a certain extent in practical applications.Therefore,the use of appropriate and fast methods to achieve chaos control is also a hot issue in research.Because of the more complex dynamic behavior of the system without equilibrium points,many classic control methods are not applicable.So the difficulty of controller design is greatly increased.For this type of system,an efficient and simple controller is designed to realize the control of the system,which has certain research value.In this paper,a new non-equilibrium point-free hyper-chaotic system with multiple types of coexisting attractors is constructed,and the proposed integer-order system is further extended to a fractional-order hyper-chaotic system.Main tasks as follows:Firstly,using Lyapunov exponential spectrum,bifurcation diagram,Poincarécross section,parameter disk,etc.,the dynamic analysis of the integer-order hyper-chaotic system is carried out.And the circuit simulation verifies the feasibility of the system.When the parameters are the same and the initial values are different,the symmetry and asymmetric attractors coexist in the system.By introducing two constants,the attractor can translate in two directions at the same time,and the type of the attractor changes during the translation process,and the system has the coexistence of chaotic attractors and periodic attractors.Secondly,on the basis of integer order,it is extended to a fractional-order hyper-chaotic system with more complex dynamics.Using Lyapunov exponential spectra and bifurcation diagrams that vary with the order and parameters to analyze the dynamics of the system,it shows that the variation of the order makes the fractional hyper-chaotic system have more types of attractors,and the individual attractors coexist.The number has increased significantly,the coexistence phenomenon is more obvious,and the fractional-order system exhibits extreme multi-stability.Finally,control the integer-order hyper-chaotic system and fractional-order hyper-chaotic system with coexistence attractors proposed in this paper.The finite time control method makes the system stable in a finite time;the neural network adaptive control method makes the system track different expected values and desired trajectories;the state feedback H_∞control can design the gain matrix through the linearization model,and use the state feedback controller to achieve the effective control of the system.The controllers designed by the three methods can stabilize the system in a very short time,and avoid the influence of the multi-stability and extreme multi-stability of the system in the actual project.