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Oscillator with Line of Equilibiria and Nonlinear Function Terms: Stability Analysis, Chaos, and Application for Secure Communications

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  • Othman Abdullah Almatroud

    (Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • Ali A. Shukur

    (Faculty of Computer Sciences and Mathematics, University of Kufa, An-Najaf 540011, Iraq)

  • Viet-Thanh Pham

    (Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City 70000, Vietnam)

  • Giuseppe Grassi

    (Department of Engineering for Innovation, University of Salento, 73100 Lecce, Italy)

Abstract

We explore an oscillator with nonlinear functions and equilibrium lines that displays chaos. The equilibrium stability and complexity of the oscillator have been analysed and investigated. The presence of multiple equilibrium lines sets it apart from previously reported oscillators. The synchronization of the oscillator is considered as an application for secure communications. An observer is designed by considering a transmitted signal as a state, in other words, by injecting a linear function satisfying Lipschitz’s condition to the proposed oscillator. Moreover, the adaptive control of the new oscillator is obtained.

Suggested Citation

  • Othman Abdullah Almatroud & Ali A. Shukur & Viet-Thanh Pham & Giuseppe Grassi, 2024. "Oscillator with Line of Equilibiria and Nonlinear Function Terms: Stability Analysis, Chaos, and Application for Secure Communications," Mathematics, MDPI, vol. 12(12), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1874-:d:1415895
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    References listed on IDEAS

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    1. Liu, Bo & Wang, Ling & Jin, Yi-Hui & Tang, Fang & Huang, De-Xian, 2005. "Improved particle swarm optimization combined with chaos," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1261-1271.
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