Building Fixed Point-Free Maps with Memristor

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, recon...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-03, Vol.11 (6), p.1319
Main Authors: Almatroud, Othman Abdullah, Pham, Viet-Thanh
Format: Article
Language:English
Subjects:
Calculus
chaos
Communication
Computer memory
Computer science
discrete map
fixed point
Generators
Initial conditions
Iterative methods
Liapunov exponents
Logic circuits
Mathematical functions
memristor
Memristors
Parameter sensitivity
Random numbers
Trends
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11061319