Abstract
It is found that the fractional order memristor model can better simulate the characteristics of memristors and that chaotic circuits based on fractional order memristors also exhibit abundant dynamic behavior. This paper proposes an active fractional order memristor model and analyzes the electrical characteristics of the memristor via Power-Off Plot and Dynamic Road Map. We find that the fractional order memristor has continually stable states and is therefore nonvolatile. We also show that the memristor can be switched from one stable state to another under the excitation of appropriate voltage pulse. The volt–ampere hysteretic curves, frequency characteristics, and active characteristics of integral order and fractional order memristors are compared and analyzed. Based on the fractional order memristor and fractional order capacitor and inductor, we construct a chaotic circuit, of which the dynamic characteristics with respect to memristor’s parameters, fractional order α, and initial values are analyzed. The chaotic circuit has an infinite number of equilibrium points with multi-stability and exhibits coexisting bifurcations and coexisting attractors. Finally, the fractional order memristor-based chaotic circuit is verified by circuit simulations and DSP experiments.
Highlights
Chua put forward the concept of memristor in 1971 [1]
In the field of memristor-based chaotic circuits, the current research achievements include memristor chaotic systems based on the titanium dioxide memristor models [4,8,9], piecewise nonlinear memristor models [10,11], quadratic nonlinear memristor model [12], local active memristors [13,14], and so on
We will discuss the equilibrium point and stability of the fractional order memristor chaotic system and the dynamic behavior of the system varying with the initial value and fractional order
Summary
Jian Wu 1 , Guangyi Wang 1, *, Herbert Ho-Ching Iu 2, *, Yiran Shen 1 and Wei Zhou 1.
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