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

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 and anti-monotonicity but also produces two new phenomena that have not been found in other chaotic systems. The first one is transient transition: the behavior of local chaos and local period transition alternately occurring. The second is state jump: the behavior of local period-4 oscillation or local chaotic oscillation jumping to local period-2 oscillation. Finally, the circuit simulation of the fractional-order multistable locally active memristive chaotic system using PSIM is carried out to verify the validity of the numerical simulation results.

Automated summary

Fractional-order calculus is used to develop a memristor with multistable locally active characteristics, showing stronger memory properties than integer-order memristors. This memristor is then applied in a chaotic system, resulting in new phenomena such as transient transitions and state jumps. Circuit simulations confirm the validity of the numerical results.