Discrete Memristor and Discrete Memristive Systems

In this paper, we investigate the mathematical models of discrete memristors based on Caputo fractional difference and G-L fractional difference. Specifically, the integer-order discrete memristor is a special model of those two cases. The " "-type hysteresis loop curves are observed when...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2022-06, Vol.24 (6), p.786
Main Authors: He, Shaobo, Zhan, Donglin, Wang, Huihai, Sun, Kehui, Peng, Yuexi
Format: Article
Language:English
Subjects:
Analysis
Circuits
Design
digital circuits
Digital electronics
discrete modeling of memristor
fractional-order difference
Hysteresis loops
Integers
Mathematical models
Memory devices
memristive system
memristor
Memristors
Methods
Numerical analysis
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Summary:In this paper, we investigate the mathematical models of discrete memristors based on Caputo fractional difference and G-L fractional difference. Specifically, the integer-order discrete memristor is a special model of those two cases. The " "-type hysteresis loop curves are observed when input is the bipolar periodic signal. Meanwhile, numerical analysis results show that the area of hysteresis decreases with the increase of frequency of input signal and the decrease of derivative order. Moreover, the memory effect, characteristics and physical realization of the discrete memristors are discussed, and a discrete memristor with short memory effects is designed. Furthermore, discrete memristive systems are designed by introducing the fractional-order discrete memristor and integer-order discrete memristor to the Sine map. Chaos is found in the systems, and complexity of the systems is controlled by the parameter of the memristor. Finally, FPGA digital circuit implementation is carried out for the integer-order and fractional-order discrete memristor and discrete memristive systems, which shows the potential application value of the discrete memristor in the engineering application field.
ISSN:1099-4300
1099-4300
DOI:10.3390/e24060786