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Building Fixed Point-Free Maps with Memristor

Author

Listed:
  • 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)

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.

Suggested Citation

  • Othman Abdullah Almatroud & Viet-Thanh Pham, 2023. "Building Fixed Point-Free Maps with Memristor," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1319-:d:1092090
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    References listed on IDEAS

    as
    1. Mazloom, Sahar & Eftekhari-Moghadam, Amir Masud, 2009. "Color image encryption based on Coupled Nonlinear Chaotic Map," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1745-1754.
    2. Wan, Qiuzhen & Li, Fei & Chen, Simiao & Yang, Qiao, 2023. "Symmetric multi-scroll attractors in magnetized Hopfield neural network under pulse controlled memristor and pulse current stimulation," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Bao, H. & Gu, Y. & Xu, Q. & Zhang, X. & Bao, B., 2022. "Parallel bi-memristor hyperchaotic map with extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    4. Jiang Wang & Yang Gu & Kang Rong & Quan Xu & Xi Zhang, 2022. "Memristor-Based Lozi Map with Hidden Hyperchaos," Mathematics, MDPI, vol. 10(19), pages 1-12, September.
    5. Amina-Aicha Khennaoui & Adel Ouannas & Shaher Momani & Othman Abdullah Almatroud & Mohammed Mossa Al-Sawalha & Salah Mahmoud Boulaaras & Viet-Thanh Pham, 2022. "Special Fractional-Order Map and Its Realization," Mathematics, MDPI, vol. 10(23), pages 1-11, November.
    6. Lazaros Moysis & Karthikeyan Rajagopal & Aleksandra V. Tutueva & Christos Volos & Beteley Teka & Denis N. Butusov, 2021. "Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map," Mathematics, MDPI, vol. 9(15), pages 1-16, August.
    7. Fei Yu & Wuxiong Zhang & Xiaoli Xiao & Wei Yao & Shuo Cai & Jin Zhang & Chunhua Wang & Yi Li, 2023. "Dynamic Analysis and FPGA Implementation of a New, Simple 5D Memristive Hyperchaotic Sprott-C System," Mathematics, MDPI, vol. 11(3), pages 1-15, January.
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    Cited by:

    1. García-Grimaldo, Claudio & Campos-Cantón, Eric, 2023. "Exploring a family of Bernoulli-like shift chaotic maps and its amplitude control," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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