Numerical Analysis And Hardware Experiment Of Special Phenomenon In Memristor-based Oscillating Systems

Memristor is a special nonlinear element with inner state variables,which is widely used in the design of chaotic oscillating circuits.In this paper,a class of oscillating circuits or systems is constructed by using memristors with different nonlinearity.The special dynamical behaviors of those circuits or systems are revealed,corresponding mechanism analysis and experiment verification are performed.Firstly,by replacing the linear resistor with a diode-bridge memristive emulator in a classical Sallen-Key filter circuit,a novel memristive oscillating circuit is proposed.Two types of oscillating behaviors are found by adjusting the negative feedback gain of the Sallen-Key low-pass filter.Based on the fast-slow analysis method,the generation mechanism of those oscillating behaviors is studied,from which an interesting phenomenon of extremely slow passage is found.The corresponding analog circuit is built for the hardware circuit experiments.Secondly,a two-memristor-based hyperchaotic system is proposed by replacing two linear resistive couplings with nonlinear memristive couplings in a BAO system.The memristive hyperchaotic system has a plane equilibrium,and the equilibrium plane is divided into three regions according to the equilibrium stability,including unstable saddle-foci,stable node and stable node-focus.The dynamical behavior of the proposed system in stability region of unstable saddle is analyzed,from which the memristor initial-offset boosting behavior is uncovered.Thereafter,the circuit of the two-memristor-based hyperchaotic system is designed,upon which the PSIM circuit experiment is confirmed.Finally,a memristor with sine memductance is introduced into a hypogenetic jerk system.The memristvie jerk system has four linear equilibrium sets,from which the periodic switched memristor initial-offset boosting phenomenon can be observed.Based on the numerical simulation methods of two-dimensional Lyapunov exponent diagram,bifurcation plot and phase portrait,the evolution feature of memristor initial-offset boosting behavior is studied.Then,the PSIM simulation experiment and hardware experiment are finished.