Dynamic Analysis And Circuit Realization Of Memristor-Based Chaotic Systems

Memristor-based chaotic system is a hot topic in the field of modern nonlinear systems.It is not only challenging in the basic research of nonlinear circuits and systems,but also has a good application prospect in many fields.This paper takes the memristor-based chaotic system as the research object,and focuses on some key scientific problems such as chaotic system construction,dynamic analysis and circuit realization and so on.In the research of the thesis,the methods of theoretical analysis,simulation and circuit design experiment are adopted respectively,and the research work is mainly carried out in the following aspects:1.The smooth system and its autonomous circuit implementation which can produce multi-wing chaotic attractors is studied.A class of chaotic smooth system based on memristor which can generate multi-winged chaotic attractors is proposed.The even order polynomial is used to construct the memristor function and the internal state variable function,and the mathematical model of this kind of three-dimensional system based on memristor is established,and the influence of system parameters on the dynamic behavior of the system is analyzed.At the same time,the relationship between the maximum number of chaotic attractors and the distribution of the"inner hole"on the plane of the phase trajectory of the subsystem is given.These results change the conclusions that the multi-wing chaotic behavior of nonlinear systems will be analyzed based on the system matrix controlled by state variables.Moreover,the effectiveness on the model producing 2 to 8 wing chaotic attractors and the validity of the theoretical analyses are confirmed by the design of the corresponding circuit implementation and circuit simulation.2.Bifurcation in a memristor-based non-inductive chaotic circuit based on active memristor which may generate hyperchaotic attractors is studied.A non-inductive hyperchaotic circuit model based on active hyperbolic memristor is established,by means of numerical analysis and central manifold theorem,the influence of the bifurcation of the memristor circuit is analyzed by the resistance R which is linearly coupled with the RC bridge oscillator and the negative resistance R_N which is used to describe the realization of the current inverter.Using the central manifold theorem,the bifurcation chaos dynamics behavior of the circuit is analyzed,including the set of equilibrium states with one or three elements,the lyapunov exponent of different symbols such as(0,0,0,-),(+,0,-,-),(+,0,0,-),and the corresponding bifurcation diagram.The results show:The bifurcation in non-inductive hyperchaotic circuits with inductive memristor is mainly caused by the resistance coupled linearly with RC bridge oscillator in the circuit and the negative resistance realized in current inverter.For high-dimensional bifurcation problems that cannot be studied by theoretical analysis,numerical analysis,for Matcont as an example is used to provide sufficient conditions for hopf-bifurcation and codimensional 2-bifurcation in memristor-based circuit system to occur as zero-hopf bifurcation,and the corresponding bifurcation points are depicted.Meanwhile,the Hopf bifurcation of the circuit model is analyzed by using the central manifold and normal form methods,and the stability and specific analytical expression of Hopf bifurcation are given,and the the effectiveness of theoretical results are verified by simulation experiment.3.The control method of chaos and fractional bifurcation in smooth system is studied.The bifurcation behavior,chaotic attractor and fractional-order chaotic controller design methods for smooth systems are analyzed by using Lyapunov exponents,Poincare mapping,power spectrum and phase trajectory.The results show:the bifurcation of a smooth system based on Liu-Chen system with multiple periodic attractors and multiple chaotic attractors is mainly caused by the change of system parameter c.Based on proper assumptions,and analyzed by analytical method and numerical method proves that any neighborhood of the four-scroll chaotic attractor contains repelling sets with the positive Lebesgue measures,points out the system of attracting basin with the riddled properties of chaotic attractor,finally,based on the stability consideration of the incommensurate fractional order system,a simple controller based on fractional order differential is designed to control the chaotic circuit of the smooth and smooth system,and the value range of the fractional order control parameter is determined when the system is stable.