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Semi-Analytical Closed-Form Solutions for Dynamical Rössler-Type System

Author

Listed:
  • 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

Mathematical models and numerical simulations are necessary to understand the functions of biological rhythms, to comprehend the transition from simple to complex behavior and to delineate the conditions under which they arise. The aim of this work is to investigate the R o ¨ ssler-type system. This system could be proposed as a theoretical model for biological rhythms, generalizing this formula for chaotic behavior. It is assumed that the R o ¨ ssler-type system has a Hamilton–Poisson realization. To semi-analytically solve this system, a Bratu-type equation was explored. The approximate closed-form solutions are obtained using the Optimal Parametric Iteration Method (OPIM) using only one iteration. The advantages of this analytical procedure are reflected through a comparison between the analytical and corresponding numerical results. The obtained results are in a good agreement with the numerical results, and they highlight that our procedure is effective, accurate and usefully for implementation in applicationssuch as an oscillator with cubic and harmonic restoring forces, the Thomas–Fermi equation and the Lotka–Voltera model with three species.

Suggested Citation

  • Remus-Daniel Ene & Nicolina Pop, 2024. "Semi-Analytical Closed-Form Solutions for Dynamical Rössler-Type System," Mathematics, MDPI, vol. 12(9), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1308-:d:1382860
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    References listed on IDEAS

    as
    1. Jator, S.N. & Mayo, D.C. & Omojola, M.T., 2021. "Block Hybrid Third Derivative Nyström type Method for Bratu’s equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 256-271.
    2. Ding, Yuting & Zheng, Liyuan, 2023. "Existence of homoclinic orbit of Shilnikov type and the application in Rössler system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 770-779.
    3. Abd-el-Malek, Mina B. & Abdelrazek, Amr & Ghazy, Mohammed & Gamal, Gehad, 2019. "A modified perturbation solution to the one-dimensional Bratu problem," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 296-304.
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