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 infinity-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.

Automated summary

This paper investigates the mathematical models of discrete memristors based on Caputo fractional difference and G-L fractional difference, and shows the hysteresis loop characteristics under different input signals. It analyzes the relationship between hysteresis area and input signal frequency and derivative order, discusses the memory effect, characteristics and physical realization of the discrete memristors, and designs a discrete memristor with short memory effects. Furthermore, discrete memristive systems are constructed by introducing fractional-order and integer-order discrete memristors, and the complexity of the systems is controlled. Finally, FPGA digital circuit implementation demonstrates the potential application value of discrete memristors in engineering applications.