Research And Design Of Multi-wing And Multi-scroll Hidden Attractor Chaotic Systems

Since the Lorenz system was proposed,scientists have found that chaotic systems have broad application prospects in secure communication,image encryption,and artificial intelligence.With the advances in technology,in order to better meet the needs of engineering applications,artificially constructing complex chaotic systems has become the focus of the current research.The multi-wing and multi-scroll chaotic systems have a wider frequency spectrum and a more complex topology than double wing and double scroll chaotic systems,which is much favored by researchers.At present,expanding the unstable equilibrium points of the systems by piecewise functions is the mainstream method for constructing multi-wing and multi-scroll chaotic systems.In recent years,as a special kind of chaotic system,hidden attractor chaotic system has been widely studied by researchers.The basin of attraction of this kind of chaotic attractor does not intersect with the neighborhood of any equilibrium point,so it is unable to locate its attractor location,therefore hidden attractor chaotic systems are more secure than ordinary attractor chaotic systems.This feature makes hidden attractor chaotic systems have important application values in the field of communication encryption.And it is also a hot research direction at present.Under this research background,this paper has studied the construction of multiwing and multi-scroll hidden attractor chaotic systems.The detailed contents are as follows:(1)A multi-wing hidden attractors chaotic system with stable equilibrium points is proposed.A multi-level pulse function is introduced into a two-wing chaotic system with two stable equilibrium points,therefore a new multi-wing hidden attractor chaotic system with multiple stable equilibrium points is constructed.By changing the number of pulses of the multi-level pulse function,chaotic attractors with even-numbered wings can be obtained.The position and number of the equilibrium points of the system are changed,but the stability of the equilibrium points is not changed.The switching behavior of the four-wing hidden attractor is studied by phase diagram and timedomain waveform diagram.And through the bifurcation graph,Lyapunov exponents,Poincaré diagram and other numerical analysis methods,the dynamic characteristics of the four-wing hidden attractor chaotic system are analyzed.In addition,the corresponding four-wing chaotic attractor simulation circuit is designed and implemented in NIMultisim software,and realized by hardware.(2)A multi-scroll chaotic system with three types of hidden attractors is proposed,which can generate multi-scroll hidden chaotic attractors with no equilibrium point,a stable equilibrium point,and multiple stable equilibrium points.By introducing a limiting piecewise linear function to expand the equilibrium points of the system,the system can generate chaotic attractors with even-numbered scrolls.On the other hand,by changing only one system parameter,the three different types of hidden attractors can be obtained.It is observed by the basin of attraction that the system's attraction domain does not intersect with the equilibrium points,so it confirms the existence of hidden attractors.At the same time,Lyapunov exponents,bifurcation diagram and Poincaré diagram are used to analyze the dynamic behaviors of the system.In addition,hardware circuit experiments are designed and completed,which verified the validity of the multi-scroll chaotic system with three types of hidden attractors.