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A Method of Qualitative Analysis for Determining Monotonic Stability Regions of Particular Solutions of Differential Equations of Dynamic Systems

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  • Vladislav V. Lyubimov

    (Department of Further Mathematics, Faculty of Mechanics and Mathematics, Natural Science Institute, Samara National Research University, 443086 Samara, Russia)

Abstract

Developing stability analysis methods for modern dynamical system solutions has been a significant challenge in the field. This study aims to formulate a qualitative analysis approach for the monotone stability region of a specific solution to a single differential equation within a dynamical system. The system in question comprises two first-order nonlinear ordinary differential equations of a particular kind. The method proposed hinges on applying elements of combinatorics to the traditional mathematical investigation of a function with a single independent variable. This approach enables the exact determination of the different qualitative scenarios in which the desired solution changes, under the assumption that the function values monotonically diminish from a specified value down to a finite zero. This paper outlines the creation and decomposition of the monotone stability region associated with the solution under consideration.

Suggested Citation

  • Vladislav V. Lyubimov, 2023. "A Method of Qualitative Analysis for Determining Monotonic Stability Regions of Particular Solutions of Differential Equations of Dynamic Systems," Mathematics, MDPI, vol. 11(14), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3142-:d:1195361
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    References listed on IDEAS

    as
    1. Mingli Xia & Linna Liu & Jianyin Fang & Yicheng Zhang, 2023. "Stability Analysis for a Class of Stochastic Differential Equations with Impulses," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
    2. Damián H. Zanette, 2018. "Stability of two-mode internal resonance in a nonlinear oscillator," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(5), pages 1-7, May.
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