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Exact Parametric and Semi-Analytical Solutions for the Rucklidge-Type Dynamical System

Author

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  • Remus-Daniel Ene

    (Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania
    These authors contributed equally to this work.)

  • Nicolina Pop

    (Department of Physical Foundations of Engineering, Politehnica University of Timisoara, 300223 Timisoara, Romania
    These authors contributed equally to this work.)

  • Rodica Badarau

    (Department of Mechanical Machines, Equipment and Transportation, Politehnica University of Timisoara, 300222 Timisoara, Romania
    These authors contributed equally to this work.)

Abstract

The behavior of the Rucklidge-type dynamical system was investigated, providing some semi-analytical solutions, in this paper. This system was analytically investigated by means of the Optimal Auxiliary Functions Method (OAFM) for two cases. An exact parametric solution was obtained. The effect of the physical parameters was investigated on the asymptotic behaviors and damped oscillations of the solutions. Damped oscillations are essential for analyzing and designing various mechanical, biological, and electrical systems. Many of the applications involving these systems represent the main reason of this work. A comparison between the obtained results via the OAFM, the analytical solution obtained with the iterative method, and the corresponding numerical solution was performed. The accuracy of the analytical and corresponding numerical results is illustrated by graphical and tabular representations.

Suggested Citation

  • Remus-Daniel Ene & Nicolina Pop & Rodica Badarau, 2025. "Exact Parametric and Semi-Analytical Solutions for the Rucklidge-Type Dynamical System," Mathematics, MDPI, vol. 13(13), pages 1-19, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2052-:d:1683898
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    References listed on IDEAS

    as
    1. Chengwei Dong & Lian Jia & Qi Jie & Hantao Li & Eric Campos, 2021. "Symbolic Encoding of Periodic Orbits and Chaos in the Rucklidge System," Complexity, Hindawi, vol. 2021, pages 1-16, August.
    2. Vignesh, D. & He, Shaobo & Banerjee, Santo, 2023. "Modelling discrete time fractional Rucklidge system with complex state variables and its synchronization," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    3. Remus-Daniel Ene & Nicolina Pop & Marioara Lapadat & Luisa Dungan, 2022. "Approximate Closed-Form Solutions for the Maxwell-Bloch Equations via the Optimal Homotopy Asymptotic Method," Mathematics, MDPI, vol. 10(21), pages 1-13, November.
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