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A Novel Chaotic System with Only Quadratic Nonlinearities: Analysis of Dynamical Properties and Stability

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  • Othman Abdullah Almatroud

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

  • Karthikeyan Rajagopal

    (Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India)

  • Viet-Thanh Pham

    (Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam)

  • Giuseppe Grassi

    (Dipartimento Ingegneria Innovazione, Universitá del Salento, 73100 Lecce, Italy)

Abstract

In nonlinear dynamics, there is a continuous exploration of introducing systems with evidence of chaotic behavior. The presence of nonlinearity within system equations is crucial, as it allows for the emergence of chaotic dynamics. Given that quadratic terms represent the simplest form of nonlinearity, our study focuses on introducing a novel chaotic system characterized by only quadratic nonlinearities. We conducted an extensive analysis of this system’s dynamical properties, encompassing the examination of equilibrium stability, bifurcation phenomena, Lyapunov analysis, and the system’s basin of attraction. Our investigations revealed the presence of eight unstable equilibria, the coexistence of symmetrical strange repeller(s), and the potential for multistability in the system.

Suggested Citation

  • Othman Abdullah Almatroud & Karthikeyan Rajagopal & Viet-Thanh Pham & Giuseppe Grassi, 2024. "A Novel Chaotic System with Only Quadratic Nonlinearities: Analysis of Dynamical Properties and Stability," Mathematics, MDPI, vol. 12(4), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:612-:d:1341372
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    References listed on IDEAS

    as
    1. Bao, B.C. & Bao, H. & Wang, N. & Chen, M. & Xu, Q., 2017. "Hidden extreme multistability in memristive hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 102-111.
    2. Jafari, Sajad & Sprott, J.C., 2013. "Simple chaotic flows with a line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 79-84.
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