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

Vladislav V. Lyubimov ()
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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

Mathematics, 2023, vol. 11, issue 14, 1-12

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.

Keywords: monotone stability; 2-function; stability region; particular solution; combinatorics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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