Nested Multi-scroll Chaotic System And Its Circuit Implementation

Chaotic system has such characteristics as pseudo-randomness,ergodicity and extreme sensitivity values and system parameters.These characteristics make chaotic systems have many potential applications.For example,the pseudo-randomness can be used in encryption.In order to apply the pseudo-randomness to chaotic secure communication better,researchers are committed to constructing chaotic systems and generating more complex chaotic attractors.At present,such exploration studies are conducted from two aspects:the first is to study new multi-scroll chaotic attractors to generating more complex chaotic signals.The second is to explore the method of generating composite attractors.A compound attractor is a combination of two or more different attractors in the phase space,so its complexity is higher.The main work of this paper is to explore nested multi-scroll chaotic systems and compound attractor chaotic systems.The concrete research contents and results summarized as follows:(1)A method of generating nested multi-scroll chaotic attractor is presented.This method only needs to add sign functions on the Jerk system.By increasing the amplitude of the sign function,the translation of the system equilibria can be achieved,so then realize the generation of nested multi-scroll chaotic attractors.The sign functions are added to the first,second,and third sub equations of the Jerk system respectively,and the system can realize nested attractors of different numbers and different nesting levels.Compared with the traditional multi-scroll chaotic attractor structure,the nested attractor structure is more complex.And the nested multi-scroll chaotic system doesn't need to construct a complicated nonlinear function,so the circuit is very simple to design.The basic dynamic characteristics of the nested multi-scroll chaotic system,such as attractor phase diagram,power spectrum and Poincare diagram,are analyzed.Based on the theoretical analysis and numerical simulation,the design and simulation of chaotic circuits are carried out,which verifies the realizability of nested chaotic attractors.Finally,the application of chaos theory in turbulent flow is discussed because the special attractor structure of nested multi-scroll is consistent with Kolmogrov's image in turbulent flow.(2)A new chaotic system that can generate composite attractors and nested attractors is proposed.We analyzed the new system about numerical simulation and theory of dynamics,including the attractor phase diagram,0-1 test chart,power spectrum,Poincare diagram,Lyapunov exponent,bifurcation diagram,etc.The system can not only generate two different composite attractors,but also can generate a nested three-scroll chaotic attractor in different system parameters.The new system has rich dynamic characteristics.Besides to generating composite attractors and nested attractors,the system can also generate multiple double-scroll chaotic attractors and coexistence attractors.Moreover,the phenomenon that that the system has a chaotic state transition can be observed by controlling the simulation time of the system.Analyzed the changes of the system state in detail when change the system parameters.