Research And Design Of Local Active Memristor And Its Fractional Order Chaos System

Fractional calculus can be said to be an extension of integer order.In real life we describe objects that tend to be fractional,and therefore more accurate using fractional calculus to describe object models compared to integer order.Memristor,called a fourth component,can be regarded as a resistance with memory function that can simulate human brain synapses.In the past few decades,with the increasing research of memristors,various types of memristors have emerged,and memristors are widely used in chaotic systems and neural networks for dynamic characteristics analysis.The principle of fractional calculus is the memory characteristics of integral or derivative to time,so fractional operations,like memristors,both have memory characteristics.Therefore,the memristor can be extended to the fractional order.Fractional order memristors are less well studied in the last decade,and most fractional order studied memristors are not rich in performance.In addition,the current research has mainly focused on continuous memristors and binary memristors,multi-value memristors have not been studied.However,a highly scalable multi-value memristors and a performance-rich fractional order memristor can better simulate synapses,produce richer kinetic properties,and its model more accurately.Therefore,designing a performance-rich fractional order memristor as well as an extended strong multi-value memristor is currently an important topic of current memristor scientific research.Based on the above analysis,this paper studies and designs the memristors,and designs a fractional order multistable local active memristor and a multistable local active multi-value memristor.In addition,these two memristors are applied to the chaotic system for dynamic analysis and simulation.The research results obtained and the main innovations of the article are as follows:(1)Put forward a fractional order multistable local active memristor,the memristor has infinite coexistence of hysteresis loop and very wide local active area.We can found that the fractional memristors has stronger memory characteristics,local active characteristics and wider non-volatile range,and this type of memristors.Based on the fractional multistable local active memristor,a simple chaotic system with rich dynamics: infinitely many equilibrium points;multistable coexistence of three attractors by changing the initial value and the bifurcation diagram.And there were two phenomena that didn’t happen in any other chaotic system.The two phenomena are transient transition and state jump respectively.Transient transition is alternating local periodic and local chaotic transfer behavior;state jump is local quadruple periodic oscillation or chaotic oscillation jump to local binary periodic oscillation.(2)A multistable locally active multi-valued memristor is proposed.The memristor is discontinuous,has an infinite number of coexisting hysteresis loop,and can change the number of discontinuity values,the shape of the hysteresis loop,and the local active region by changing the initial value.Therefore,we can design multistable local active memristors with two,three,four,or even multiple values by changing the initial value,with strong scalability.In addition,the effect of the initial value change on the memristor characteristics is analyzed mathematically.We propose a simple fractional order chaotic system based on this multistable locally active multi-valued memristors and study the influence of the system parameters and fractional order on the dynamical properties,and study the rich dynamical behavior of the system through phase diagram,bifurcation diagram,and Lyapuov exponential spectral.