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 the fractional-order multistable locally active memristive chaotic system using PSIM is carried out to verify the validity of the numerical simulation results.

Firing activities in a fractional-order Hindmarsh–Rose neuron with multistable memristor as autapse

“…(d) Phase diagrams, where black, red and green respectively represent the initial value of (1, 0, 0, -4), (1, 0, 0, 0) and (1, 0, 0, 4)). In a fractional-order system, if the trajectory of the system is A-periodic oscillation in some intervals, while the trajectory of other adjacent regions is chaotic, this phenomenon is called "local chaos" [35]. From Fig.…”

“…Xie et al proposed a fractional-order memristor with infinite locally active interval and coupled it to Chen's chaotic system. They found that the system presents different states under different fractional orders [35]. However, so far, there is no relevant research on fractional-order neuron model with locally active memristor.…”

Fully Integrated Chen Chaotic Oscillation System

“…With the development of nonlinear systems, the research on chaos and chaotic neural networks has grown rapidly in recent years [1][2][3][4][5][6][7][8][9][10]. However, the development of chaos and chaotic neural networks mainly focuses on their software algorithm improvement [11][12][13][14][15][16][17][18], the hardware implementation of chaos and chaotic neural networks has fallen far behind their software algorithm.…”

A Novel Fractional-Order Discrete SIR Model for Predicting COVID-19 Behavior

“…In mathematical analysis, fractional calculus is considered one of the most important subjects as a generalization of integer calculus [25][26][27][28][29][30]. It has been demonstrated that the fractional-order derivative is significantly more precise than the integer-order one [31]. This is because it plays a key role as a powerful tool for outlining the effect of memory on all kinds of materials and processing [32].…”