Eur. Phys. J. Spec. Top. (2022) 231: 3197-3207
https://doi.org/10.1140/epjs/s11734-022-00567-w

Regular Article

Discrete fracmemristor model with the window function and its application in Logistic map

¹ Xi’an Key Laboratory of Advanced Photo-electronics Materials and Energy Conversion Device, School of Science, Xijing University, 710123, Xi’an, People’s Republic of China
² Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source, School of Science, Xijing University, 710123, Xi’an, People’s Republic of China

^b williamchristian@163.com

Received: 5 November 2021
Accepted: 3 April 2022
Published online: 22 April 2022

Abstract

In recent years, the mathematical model of memristor has attracted extensive attention from researchers, but the boundary effect of the memristor model is rarely considered. A memristor with the window function is proposed in this paper. First, the boundary effect of the device is ignored by the conventional memristive model, but the memristor model with the window function can effectively solve this problem. Then, based on the fractional difference theory, a discrete fractional mathematical model of memristor with the window function is studied. Meanwhile, the corresponding three memristor characteristics are verified for this model in the numerical simulations. Finally, the discrete fractional memristor model is applied to the Logistic map, and we construct a new chaotic map called the discrete fracmemristor Logistic map. The new chaotic sequence is observed. In addition, it provides important mathematical models for many fields, such as chaotic systems, chaotic circuits, and neural networks.