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

Othman Abdullah Almatroud, Ali A. Shukur, Viet-Thanh Pham () and Giuseppe Grassi
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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

Mathematics, 2024, vol. 12, issue 12, 1-18

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.

Keywords: equilibrium; stability; chaos; Banach space; communications (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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