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Multiple attractors in a novel simple 4D hyperchaotic system with chaotic 2-torus and its circuit implementation

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Abstract

In \(n\)-dimensional systems, finding of \((n-2)\) positive Lyapunov exponents (LEs) with the largest Lyapunov exponents is more motivating, vital, and hard compared to other traditional systems. A new simple unusual 4-dimension system with \((n-2)\) positive Lyapunov exponents has been derived from the popular Sprott S system by utilizing a state feedback controller. The proposed system has one stable/unstable equilibrium point and is featured to have two attractors: self-excited and hidden, besides having a rare behavior of a chaotic with 2-torus. Dynamic properties are established through theoretical results and numerical simulation which include equilibrium points, stability, phase portraits, and the Lyapunov spectrum. Routh–Hurwitz criteria for stability and Wolf algorithm also indicate that the new system has a multi-attractor and is highly efficient; these results are better than the famous 3D Sprott S system and can be used in various applications. Moreover, the system's feasibility was demonstrated by implementing its anti-synchronization. Furthermore, the corresponding analog electronic circuit of the proposed system is designed and simulated on the Multisim 14.2 software.

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Authors and Affiliations

  1. Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq

    Saad Fawzi Al-Azzawi & Maryam A. Al-Hayali

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  1. Saad Fawzi Al-Azzawi
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  2. Maryam A. Al-Hayali
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Correspondence to Saad Fawzi Al-Azzawi.

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Al-Azzawi, S.F., Al-Hayali, M.A. Multiple attractors in a novel simple 4D hyperchaotic system with chaotic 2-torus and its circuit implementation. Indian J Phys 97, 1169–1179 (2023). https://doi.org/10.1007/s12648-022-02483-0

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