Dynamic Analysis And Circuit Implementation Of Chaotic System With Periodic Excitation

With the rapid development of chaos science,the dynamic analysis and application of non-autonomous chaotic systems have gradually become one of the hot topics in the field of nonlinear science.Considering the particularity of time-varying equilibrium point in non-autonomous chaotic systems,there are many complex nonlinear dynamics phenomena in non-autonomous chaotic systems.Therefore,in this paper,the chaotic dynamics and multi-time scale dynamics of three kinds of periodically excited chaotic systems are systematically studied by combining a variety of qualitative and quantitative nonlinear dynamics analysis methods,and the specific work can be summarized as follows:(1)An autonomous Lorenz-like chaotic system is studied.Firstly,a non-autonomous chaotic system with parametric excitation is constructed by introducing parametric excitation.Secondly,the dissipation,symmetry and equilibrium stability of the system are analyzed theoretically.Then,the effects of the excitation frequency and initial value and the initial value of the state variable on the system dynamics were studied by using these tools such as phase trajectory diagram,bifurcation diagram and Lyapunov exponential spectrum.The complex phenomenon of bursting-oscillation in the system is also revealed.Finally,the complex dynamic behavior of the system is verified by using Multisim simulation software and DSP development board.(2)Based on the classical Sprott C chaotic system,by introducing trigonometric function and external excitation,an external excitation non-autonomous chaotic system with extremely multistability is constructed.The periodic properties of trigonometric functions cause the system to produce an infinite number of symmetric equilibria point with periodic intervals of 2?,with time-varying stability.Then,the effect of excitation amplitude and frequency on system dynamics behavior is analyzed by using these tools such as phase diagram,bifurcation diagram,bifurcation diagram with double initial value and Lyapunov exponential spectrum.The infinite number of symmetrically coexisting chaotic attractors and bursting oscillations are verified.Finally,the chaotic system is realized by designing an analog circuit,and chaotic attractor and bursting oscillation are realized physically.(3)A novel Lorenz-like autonomous system with multi-timescale is studied.Firstly,a non-autonomous chaotic system model of parameter-external joint excitation is constructed by introducing the parameter-external joint excitation.Secondly,using the sequence diagrams,transformation phase diagram related to excitation,bifurcation diagram and Lyapunov exponential spectrum to study novel period,quasi periodic and chaotic bursting oscillation induced by pitchfork/Hopf/homoclinic bifurcation cascade.Meanwhile,the formation mechanism of bursting oscillation is analyzed in detail by means of generalized fast-slow analysis method.Finally,the above cascade bursting oscillations are physically verified by using the combination of Multisim simulation software and analog circuit experiment.