A fractional-order multistable locally-active memristor and its chaotic system with transient transition, state jump

Abstract Fractional calculus is closer to reality and has the same memory characteristics as memristor. Therefore, a fractional-order multistable locally active memristor is proposed for the first time in this paper, which has infinitely many coexisting pinched hysteresis loops under different initial states and wide locally active regions. Through the theoretical and numerical analysis, it is found that the fractional-order memristor has stronger locally active and memory characteristics and wider nonvolatile ranges than the integer-order memristor. Furthermore, this fractional-order memristor is applied in a chaotic system. It is found that oscillations occur only within the locally active regions. This chaotic system not only has complex and rich nonlinear dynamics such as infinitely many discrete equilibrium points, multistability, anti-monotonicity but also produces two new phenomena that have not been found in other chaotic systems after neglecting some initial transients. The first one is transient transition: the behavior of transient chaotic and transient period transition alternately occurring. The second is state jump: the behavior of period-4 oscillation or chaotic oscillation jumping to period-2 oscillation.Finally, the circuit simulation of fractional-order multistable locally active memristive chaotic system using PSIM is carried out to verify the validity of the numerical simulation results.