An Oscillator without Linear Terms: Infinite Equilibria, Chaos, Realization, and Application

Othman Abdullah Almatroud, Victor Kamdoum Tamba, Giuseppe Grassi 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
Victor Kamdoum Tamba: Department of Telecommunication and Network Engineering, Fotso Victor University Institute of Technology, University of Dschang, Bandjoun P.O. Box 134, Cameroon
Giuseppe Grassi: Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy
Viet-Thanh Pham: Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam

Mathematics, 2021, vol. 9, issue 24, 1-15

Abstract: Oscillations and oscillators appear in various fields and find applications in numerous areas. We present an oscillator with infinite equilibria in this work. The oscillator includes only nonlinear elements (quadratic, absolute, and cubic ones). It is different from common oscillators, in which there are linear elements. Special features of the oscillator are suitable for secure applications. The oscillator’s dynamics have been discovered via simulations and an electronic circuit. Chaotic attractors, bifurcation diagrams, Lyapunov exponents, and the boosting feature are presented while measurements of the implemented oscillator are reported by using an oscilloscope. We introduce a random number generator using such an oscillator, which is applied in biomedical image encryption. Moreover, the security and performance analysis are considered to confirm the correctness of encryption and decryption processes.

Keywords: chaos; nonlinear oscillations; bifurcation diagram; analog circuit; random number generator; biomedical image encryption (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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