Modeling and Analysis of the Monotonic Stability of the Solutions of a Dynamical System

Abstract

This study aims to develop an approach for the qualitative analysis of the monotonic stability of specific solutions in a dynamical system. This system models the motion of a point along a conical surface, specifically a straight and truncated circular cone. It consists of two nonlinear ordinary differential equations of the first order, each in a unique form and dependent on a particular parameter. Our proposed method utilizes traditional mathematical analysis of a function with a single independent variable, integrated with combinatorial elements. This methodology enables the precise determination of various qualitative cases where the chosen function's value monotonically decreases as a point moves along the conical surface from a specified starting point to a designated point within a final circular region. We assume that the system's partial solutions include a finite number of inflection points and multiple linear intervals.