Dynamics Analysis And Synchronization Study Of Chaotic Systems With Hidden Attractors

Since Lorenz first discovered chaos in 1963 while studying atmospheric convection phenomena,chaos theory has gradually become a hot topic of research and has been widely applied.The discovery of hidden attractor has attracted a great deal of attention from scholars,compared to traditional self-excited attractor,the attraction domains of the hidden attractor does not intersect with of any equilibrium point neighborhood,therefore cannot be localized by standard computational procedures.Due to this special hidden property and complex dynamical behavior,hidden attractor is of great importance in both chaos theory and practical applications.In this paper,an extended Sprott C chaotic system with stable equilibrium points is proposed,and the range of equilibrium points stability of the system with the variation of two parameters is determined according to the Routh-Hurwitz criterion.The hidden behavior of the system is investigated by adjusting the parameters.As the stability of the equilibrium point changes,it is found that there are two cases of hidden attractors and self-excited attractors under the asymmetric equilibrium points,and only self-excited attractors under the symmetric equilibrium points,and the hidden attractor of the system is verified through the attraction domain cross-section.A four-dimensional Sprott B chaotic system that can produce coexisting hidden attractors is proposed,which can produce rich dynamical properties,including coexistence of periodic attractors,coexistence of periodic attractors and chaotic attractors,and coexistence of chaotic attractors.The dynamical properties of two chaotic systems are analyzed in terms of phase diagrams,bifurcation diagrams,and Lyapunov exponential spectrums,and the offset boosting of variables is achieved by adjusting a control constant.The complexity spectrums of two systems with parameters variation are calculated using the fuzzy entropy algorithm,the C0 algorithm and the spectral entropy algorithm.The circuit model of the system is designed using Multisim software to perform simulation experiments,and the circuit simulation of the hidden attractors and self-excited attractors are realized,which are consistent with MATLAB numerical simulation results.The state observer synchronization method and self-synchronization method are used to study the synchronization of the expanded Sprott C system,and the adaptive synchronization method and complete state projection synchronization method are used to study the synchronization of the four-dimensional Sprott B system,the suitable controllers are designed to make the two chaotic systems both achieve their complete synchronization.On the basis of the synchronization,the synchronization circuits are designed and the synchronization circuit simulation is completed.