Building Fixed Point-Free Maps with Memristor

Othman Abdullah Almatroud () and Viet-Thanh Pham
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Othman Abdullah Almatroud: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Viet-Thanh Pham: Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam

Mathematics, 2023, vol. 11, issue 6, 1-11

Abstract: A memristor is a two-terminal passive electronic device that exhibits memory of resistance. It is essentially a resistor with memory, hence the name “memristor”. The unique property of memristors makes them useful in a wide range of applications, such as memory storage, neuromorphic computing, reconfigurable logic circuits, and especially chaotic systems. Fixed point-free maps or maps without fixed points, which are different from normal maps due to the absence of fixed points, have been explored recently. This work proposes an approach to build fixed point-free maps by connecting a cosine term and a memristor. Four new fixed point-free maps displaying chaos are reported to illustrate this approach. The dynamics of the proposed maps are verified by iterative plots, bifurcation diagram, and Lyapunov exponents. Because such chaotic maps are highly sensitive to the initial conditions and parameter variations, they are suitable for developing novel lightweight random number generators.

Keywords: chaos; fixed point; discrete map; memristor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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