Research On Multi-scroll Chaotic Hidden Attractors And Its Synchronization

Chaos is an explicit,seemingly irregular and complex behavior caused by the internal causes of a deterministic system.The most important characteristic of chaos is its extreme sensitivity to the initial values and parameters of the system,which makes it have great potential applications in the fields of secure communication and image encryption.Chaotic signal can be generated by nonlinear circuit and has practical application value.The chaotic signals generated by the multi-scroll chaotic system show more complex dynamic characteristics,so the multi-scroll chaotic system has better application potential.Therefore,the research and circuit implementation of multi-scroll chaotic systems have attracted the attention of a large number of researchers.At present,the dissipative chaotic systems are mainly divided into self-excited attractor system and hidden attractor system.The multi-vortexization of self-excited attractor subsystem is studied more,but the multi-vortexization of hidden attractor chaotic system is paid less attention.In this paper,we mainly study the multivortexization and synchronization of hidden attractors.By means of theoretical analysis,numerical simulation,circuit design and actual circuit fabrication,three different types of chaotic systems with hidden attractors are studied.Specific research contents are as follows:(1)The sigmoid function is used to construct the multi-stage impulse function,and the constructed impulse function is added to the corresponding system equation to realize the multi-volumization of chaotic attractor: 1)In the chaotic system of hidden attractor with stable equilibrium points,the number of stable equilibrium points is extended,but the stability is not affected,and the number of vortex volumes of hidden attractor is increased;2)In the chaotic system of hidden attractor without equilibrium point,the number of equilibrium points in the system equation is not changed by adding the constructed multi-level function,and the reformed system still has no equilibrium point,and the multi-volumization of hidden attractor without equilibrium point is realized;3)In the hyperchaotic system of hidden attractor without equilibrium point,adding the multi-level function of the constructed system does not change the number of equilibrium points of the system equation,and there is still no equilibrium point in the reformed system.The multi-volumization of hidden attractor hyperchaotic system without equilibrium point is realized.(2)Compared with the traditional functions used to generate multi-scroll chaotic attractors,the sigmoid function is smooth and continuous,so it is easier to implement the analog circuit.A four-dimensional hidden attractor chaotic system with no equilibrium is taken as an example,a unidirectional multi-scroll chaotic system circuit is designed by using the exponential circuit,division circuit summation circuit and other modules.And the hardware circuit is used to realize it.The numerical simulation results and the simulation results of Multisim circuit are in complete agreement with the circuit test results.(3)Study the chaotic synchronization of different types of hidden attraction subsystems.According to the adaptive control method and Lyapunov stability theorem,an efficient,simple and stable synchronization scheme is proposed.According to this scheme,the synchronization between chaotic systems with the same hidden attractor and the synchronization between chaotic systems with different hidden attractor structures are studied.The feasibility of the proposed synchronization scheme is verified on the Matlab platform,and this method can indeed realize the synchronization of chaotic systems with hidden attractors.