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Open AccessArticle

A Nonvolatile Fractional Order Memristor Model and Its Complex Dynamics

1
Institute of Modern Circuit and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China
2
School of Electrical, Electronic, and Computer Engineering, The University of Western Australia, Perth, WA 6009, Australia
*
Authors to whom correspondence should be addressed.
Entropy 2019, 21(10), 955; https://doi.org/10.3390/e21100955
Received: 26 August 2019 / Revised: 25 September 2019 / Accepted: 27 September 2019 / Published: 29 September 2019
(This article belongs to the Special Issue Entropy, Nonlinear Dynamics and Complexity)
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. View Full-Text
Keywords: chaos; memristor; fractional order; complex dynamics chaos; memristor; fractional order; complex dynamics
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Wu, J.; Wang, G.; Iu, H. .-C.; Shen, Y.; Zhou, W. A Nonvolatile Fractional Order Memristor Model and Its Complex Dynamics. Entropy 2019, 21, 955.

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