The Research Of Novel Chaotic System With Invariable LE Spectrum And Memristive Hyperchaotic System With Hidden Attractor

On the one hand,compared with other ordinary chaotic system,a novel chaotic system with the characteristic of invariable Lyapunov exponent(LE)spectrum can not only exhibit a excellent robustness of chaos,but also its success in achieving the amplitude of chaotic signal stretching or narrowing.However,most of the existing systems only have the characteristics of constant LE spectrum for one parameter or two parameters,and these systems still have the shortcomings of limited evolution freedom and generally low positive LE value.On the other hand,by adding memristor to the different nonlinear dynamical systems,we can obtain a quantity of memristive hyperchaotic systems with hidden chaotic or hidden hyperchaotic attractor,and result in the appearance of the coexistence of hidden attractors or infinitely many hidden attractors.At present,the most of these existing systems are just concentrated in four-dimensional hyperchaotic systems,while there are more key's parameters and remarkable dynamical behaviors in the high-dimension-al hyperchaotic systems.Therefore,We have a research on two crucial importance issues,which are designing a novel chaotic system with both multi-parameter invariable LE spectrum and larger positive LE value,and constructing high-dimensional memristive hyperchaotic system with hidden attractor.The main research work of this paper is summarized as follows:(1)A novel unified chaotic system with invariable LE spectrum is proposed,which can generate the four new types of two-wing chaotic attractors with the characteristic of multi-parameter invariable LE spectrum and larger positive LE value.Firstly,some main dynamical characteristics of this new system are analyzed by using the conventional numerical analysis method.Secondly,the system parameters influencing on chaotic system is discussed through LE spectrum,bifurcation diagrams and chaotic signal amplitude.It is found that the unified chaotic system not only has unique and complex dynamic characteristics including period-doubling bifurcation,fixed point,period and chaos,but also has the functions of the global andlocal nonlinear amplitude modulation parameters.Thirdly,taking the first chaotic attractor of system as an example by introducing the two new types of nonlinear functions,the expansion of grid multi-wing attractor is realized.Finally,the hardware circuit of novel unified chaotic system is designed,and the four new types of chaotic attractors are observed experimentally,which are consistent with numerical simulation results.(2)A novel memristive hyperchaotic system with hidden attractor is introduced,which can produce hyperchaos,the coexistence of hidden attractor and infinitely many hidden attractors.This new system does not display any equilibrium point,but it can exhibit the attractive phenomenon of extreme multistability with the coexistence of infinitely many hidden attractors.By means of numerical simulation,the remarkable hidden dynamical behaviors depending on parameters of the system are discussed,such as periodic,chaotic,intermittent chaotic,hyperchaotic and transient hyperchaotic behavior.In addition,the striking phenomenon of extreme multistability relying on memristor initial condition is emphatically investigated.Meanwhile,An amazing and interesting feature of the convenience of offset boosting control can be observed in the memristive hyperchaotic system as well.Finally,a hardware electronic circuit of the system is constructed and some relevant experiments are carried out.