Research And Design Of Multi-wing And Multi-scroll Hidden Attractor Chaotic Systems With Stable Equilibrium Points

In the last three decades,in order to increase the complexity of chaotic systems,a lot of multi-wing and multi-scroll chaotic attractors were generated by designing the nonlinear function of chaotic systems.Multi-wing attractors and multi-scroll attractors are more suitable for the application of encryption,for t he reason that multi-wing attractor and multi-scroll attractor have better randomness compared with the classical attractors.Therefor,it is of great value to study the method of generating multi-wing and multi-scroll attractors.A typical and important m ethod to generate multi-wing and multi-scroll attractors is that increasing the number of unstable equilibrium points of chaotic systems ensure s the generation of multi-wing and multi-scroll attractors.In the past decade,although some hidden attractor ch aotic systems have been discovered,such as those with stable equilibrium points,those without equilibrium points and those with infinite equilibrium point s,it will be a big challenge to construct the hidden attractor s with multi-wings and multi-scrolls.It is of great esscential to study the method to generate multi-wing and multi-scroll hidden attractors.Hidden attractors not only have important research value in chaos theory,but also play an important role in engineering applications.For example,hidden attractor can generate unexpected and potentially disastrous responses to perturbations in a structure like a bridge or an airplane wing.The hidden characteristic of the hidden attractor makes it difficult to attrack through the phase space reconstruction in the application of chaotic encryption,thereby increasing the security of chaotic encryption.Therefore,the construction of multi-wing and multi-scroll hidden attractors is an important topic in research and application of chaotic science.Based on the reasearchings of chaotic systems with hindden attractors,multi-wing chaotic systems and multi-scroll chaotic system,a multi-wing hidden attractor chaotic system with smooth function and a multi-scroll hidden attractor chaotic system with piecewise linear functio n are proposed.The main innovations of this thesis are as follows:(1)A multi-wing hidden attractor chaotic system with smooth f unction is proposed.The equilibrium points of the proposed system are analysised,and the influence of system parameters on the stability of equilibrium points are analysised by number simulation.The proposed system has only one stable equilibrium point,however,it can generate four-wing attractor,one-wing attractor and coexisting of quasi-periodic and periodic attractor.An attraction basin of attractors is choosen,to verify the chaotic attractors generated by the proposed system with only one stable equilibrium point are hidden attractors.The Lyapunov exponents are used to stud y the nonlinear dynamics of the proposed system.Finally,an electronic circuit is designed to implement the chaotic system.The results of hardware circuit are in good agreements with the Matlab simulations.(2)A multi-scroll hidden attractor chaotic system with piecewise linear function is proposed.It is confirmed that the proposed system has only two stab le quilibrium points.However,the proposed system can generate multi-scroll chaotic attractors that the number of scrolls increasing with the number of breakpoints of piecewise linear function.The relationship between two equilibrium points and the attraction basin is studied to verify that the proposed multi-scroll attractors are hidden attractors.The Lyapunov exponents and bifurcation diagram are used to study the dynamics of the proposed system.Finally,an electronic circuit experiment of the multi-scroll hidden attractors is performed.