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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Othman Abdullah Almatroud & Victor Kamdoum Tamba & Giuseppe Grassi & Viet-Thanh Pham, 2021. "An Oscillator without Linear Terms: Infinite Equilibria, Chaos, Realization, and Application," Mathematics, MDPI, vol. 9(24), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3315-:d:706324
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    References listed on IDEAS

    as
    1. Jose Cruz Nuñez-Perez & Vincent Ademola Adeyemi & Yuma Sandoval-Ibarra & F. Javier Pérez-Pinal & Esteban Tlelo-Cuautle, 2021. "FPGA Realization of Spherical Chaotic System with Application in Image Transmission," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-16, April.
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    Cited by:

    1. Jiri Petrzela, 2022. "Chaos in Analog Electronic Circuits: Comprehensive Review, Solved Problems, Open Topics and Small Example," Mathematics, MDPI, vol. 10(21), pages 1-28, November.
    2. Luigi Fortuna & Arturo Buscarino, 2022. "Analog Circuits," Mathematics, MDPI, vol. 10(24), pages 1-4, December.

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