Eur. Phys. J. Plus (2022) 137: 211
https://doi.org/10.1140/epjp/s13360-022-02433-z

Regular Article

Constructing non-fixed-point maps with memristors

¹ Centre for Artificial Intelligence, Chennai Institute of Technology, Chennai, India
² Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi, Algeria
³ Department of Telecommunication and Network Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, Dschang, Cameroon
⁴ Dipartimento Ingegneria Innovazione, Universita del Salento, Lecce, Italy
⁵ Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
⁶ Department of Mathematics, Faculty of Science, University of Jordan, Amman, Jordan
⁷ Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

^f phamvietthanh@tdtu.edu.vn

Received: 28 November 2021
Accepted: 30 January 2022
Published online: 8 February 2022

Abstract

Chaotic maps, memristive maps, and maps with special fixed points have attracted significant researches recently. We introduce a simple methodology to construct a memristor-based map without fixed points in this work. In our methodology, a tiny perturbation is included into a memristor-based map to change its fixed points. Therefore, the presence and disappearance of fixed points can be controlled. By considering two general structures of discrete maps, seven memristive non-fixed-point maps have been reported. We have found that the methodology is useful for designing not only non-fixed-point maps with memristor but also non-fixed-point maps without memristor. To confirm the physical realization of the proposed maps, a hardware implementation of one of such maps is performed using a microcontroller.