Study On Bursting Behaviour And Bifurcation Mechanism In Two Time-scale Memristor Systems

The characteristics of the multi-time scale coupling system is that it can be widely used in engineering background and engineering applications,which has attracted the attention of scholars and become a hot research topic in recent years.Although nonlinear systems based on memristive have attracted worldwide attention in recent years,the bursting oscillation research in memristor-based systems still needs further exploration.Based on this background,this dissertation has performed related work based on the bursting phenomenon and its mechanism of multi-time scale coupled memristive systems.The specific content is as followsFirst,we built a memristor-based Shimizu-Morioka system by adding an external AC excitation,the bursting oscillations and bifurcation mechanism in a memristorbased Shimizu-Morioka system are explored when the value of the external excitation frequency is far less than the natural frequency of the system.In memristor-based Shimizu-Morioka system,we mainly conduct the following research: The bifurcation properties of the fast system are exploited by considering the periodic excitation as a slow-varying parameter.The various critical values of fork bifurcation,various different attractors are obtained respectively Complex bursting oscillators are revealed when the slow-varying parameter passes through these critical values.The corresponding bifurcation mechanism,namely,symmetric Fold/Fold,symmetric compound Fold/Fold-delayed sup Hopf/sup Hopf,symmetric compound sub Hopf /sub Hopf-sup Hopf/sup Hopf,symmetric sub Hopf /sub Hopf,sup Hopf/saddle on limit cycle,symmetric delayed sup Hopf /delayed sup Hopf,symmetric delay sup Hopfsup Hopf/sup Hopf are analyzed by the transformed phase portraits,the time series,and the phase portraits.The effect of the external excitation frequency on the symmetric Fold/Fold bursting in the memristive S-M system is revealed.Finally,provide some numerical and circuit simulation results to achieve the correct and effective purpose of the verification study.A memristor-based Jerk system with parametric excitation is proposed in next study.As the selected excitation frequency is far less than the natural frequency,implying the existence of an order gap between the excitation frequency and the natural one,the system can be considered as a classic fast-slow system with two timescales.In memristor-based Jerk system,me mainly conduct the following research: In my system,when the slow-varying parameters periodically pass through the critical pitchfork bifurcation point periodically,a distinct time delay behavior can be observed.Complex bursting oscillations induced by the delayed pitchfork are revealed with different excitation amplitudes.With the help of transformation phase diagrams and fast and slow analysis methods,time series and phase diagrams,the corresponding mechanism of bursting mechanism generation is discussed.As the delay time interval induced by the pitchfork bifurcation is dependsnot only on the excitation amplitude,but also on the excitation frequency,some excitation frequency related bursting patterns are also considered in our study.Finally,the numerical simulation is also completed by using MATLAB,and the results support the correctness and validity of the theoretical research.