Modeling,Dynamics Analysis And Realization Of Memristive Chaotic System

In 2008,HP Laboratories in the United States announced that the fourth fundamental circuit element,memristor,was made on the nanoscide for the first time.This major breakthrough immediately triggered a boom in research on memristive materials,models and applications at home and abroad.Memristor has shown great application value in non-volatile memories,artificial neural networks,non-linear circuit systems and other fields because of its special memory.In the field of nonlinear systems,the newly constructed memristive nonlinear circuit system can generate chaotic signals with high complexity and strong randomness required for secure communication and image encryption.What‘s more,its efficiency,security and confidentiality are higher than the general chaotic circuit system.Therefore,it has important application value and practical significance to construct a new memristor chaotic system with complex dynamic behavior.In this paper,two novel memristor chaotic systems are constructed based on different memristor models,and the theoretical analysis and research of the newly constructed memristive chaotic system are carried out.Futhermore,the corresponding memristive chaotic circuit is designed based on the constructed system.The feasibility and physical implementability of the hardware circuit and DSP hardware platform were experimentally verified.The specific content is summarized as follows:(1)A four-wing memristive Liu-Chen chaotic system with attractor rotation is constructed by introducing a secondary magnetron memristor model as the feedback term of the classic Liu-Chen system.Then,the conventional dynamics analysis of the phase diagram,bifurcation diagram,basin of attraction,Lyapunov exponent,etc.of the system is carried out,it was found that this memristive chaotic system with a line of equilibrium can generate a novel phenomenon of coexisting attractor rotation in various states by changing the initial value of memristor,as well as complex dynamic behaviors such as transient transition and sustained chaotic state of other coexisting attractors.Then,the corresponding circuit design,simulation and hardware experiment of the proposed memristive chaotic system are carried out.The circuit simulation and experimental results are basically consistent with the results of numerical theory simulation analysis.Subsequently,taking this memristive liu-chen chaotic system as the research object,the system is fractionalized..Then,a reasonable fractional-order controller was designed based on the finite-time stability theorem to realize the fractional-order memristive Finite time synchronization of Liu-Chen chaotic system.(2)By introducing a hyperbolic tangent memristor to the Holmes type Duffing equation,a hyperbolic tangent memristive Duffing system is obtained.By analyzing the phase diagram,transformed phase portrait,bifurcation diagrams and so on,it was revealed that the system has the hot issues of bursting phenomenon and other abundant dynamic behaviors in current neural network research.For example,when the frequency F of external excitation is changed,this system can present non-symmetrical bilateral bursting,bursts with controllable number of oscillation spikes,non-symmetrical unilateral coexisting bursting,as well as the diverse coexistence of periodic chaos and other dynamic behaviors.Then,the mechanism of bursting oscillation is studied by analysis of equilibrium point and bifurcation diagram..The hardware implementation of the system is carried out by using Multisim circuit simulation and digital signal processing platform(DSP),and the experimental results are consistent with the theoretical analysis,thus verifying the feasibility and physical realizability of the system.