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Approximate Closed-Form Solutions for a Class of 3D Dynamical Systems Involving a Hamilton–Poisson Part

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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.)

Abstract

The goal of this paper is to build some approximate closed-form solutions for a class of dynamical systems involving a Hamilton–Poisson part. The chaotic behaviors are neglected. These solutions are obtained by means of a new version of the optimal parametric iteration method (OPIM), namely, the modified optimal parametric iteration method (mOPIM). The effect of the physical parameters is investigated. The Hamilton–Poisson part of the dynamical systems is reduced to a second-order nonlinear differential equation, which is analytically solved by the mOPIM procedure. A comparison between the approximate analytical solution obtained with mOPIM, the analytical solution obtained with the iterative method, and the corresponding numerical solution is presented. The mOPIM technique has more advantages, such as the convergence control (in the sense that the residual functions are smaller than 1), the efficiency, the writing of the solutions in an effective form, and the nonexistence of small parameters. The accuracy of the analytical and corresponding numerical results is illustrated by graphical and tabular representations. The same procedure could be successfully applied to more dynamical systems.

Suggested Citation

  • Remus-Daniel Ene & Nicolina Pop, 2023. "Approximate Closed-Form Solutions for a Class of 3D Dynamical Systems Involving a Hamilton–Poisson Part," Mathematics, MDPI, vol. 11(23), pages 1-26, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4811-:d:1289964
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    References listed on IDEAS

    as
    1. Lu, Yang & Gong, Mengxin & Gan, Zhihua & Chai, Xiuli & Cao, Lvchen & Wang, Binjie, 2023. "Exploiting one-dimensional improved Chebyshev chaotic system and partitioned diffusion based on the divide-and-conquer principle for 3D medical model encryption," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    2. Yildirim, Gokce & Tanyildizi, Erkan, 2023. "An innovative approach based on optimization for the determination of initial conditions of continuous-time chaotic system as a random number generator," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    3. Remus-Daniel Ene & Nicolina Pop, 2023. "Semi-Analytical Closed-Form Solutions for the Rikitake-Type System through the Optimal Homotopy Perturbation Method," Mathematics, MDPI, vol. 11(14), pages 1-22, July.
    4. Lai, Qiang & Chen, Zhijie, 2023. "Grid-scroll memristive chaotic system with application to image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
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