ac7ec2ab-fed4-4650-a6b0-ae26c3b8953120240123101153396wseas:wseasmdt@crossref.orgMDT DepositPROOF2732-99412944-916210.37394/232020https://wseas.com/journals/proof/index.php22020232202023310.37394/232020.2023.3https://wseas.com/journals/proof/2023.phpVladislv V.LuybimovDepartment of Further Mathematics, Samara National Research University, 34, Moskovskoe shosse, Samara, 443086 RUSSIAThis 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.1231202312312023848912https://wseas.com/journals/proof/2023/a24proof-009(2023).pdf10.37394/232020.2023.3.12https://wseas.com/journals/proof/2023/a24proof-009(2023).pdf10.3390/sym15030709R. R. Cuzinatto, R. P. Gupta and P. J. Pompeia, Dynamical Analysis of the Covarying Coupling Constants in Scalar–Tensor Gravity,Symmetry , Vol. 15, 2023. 10.3390/axioms12030315K. Zhao, Existence and Stability of a Nonlinear Distributed Delayed Periodic AG-Ecosystem with Competition on Time Scales, Axioms, Vol.12, 2023. 10.3390/fractalfract7040288W. Yan, Z. Jiang, X. Huang and Q. Ding, Adaptive Neural Network Synchronization Control for Uncertain Fractional-Order TimeDelay Chaotic Systems, Fractal Fractional. Vol. 7, 2023. 10.3390/act12030111B. Chen, R. Zhang, F. Zhou and W. Du, An Observer-Driven Distributed Consensus Braking Control Method for Urban Railway Trains with Unknown Disturbances, Actuators, Vol. 12 , 2023. 10.3390/sym14102135V.V. Lyubimov, Method of an Asymptotic Analysis of the Nonlinear Monotonic Stability of the Oscillation at the Problem of Damping of the Angle of Attack of a Symmetric Spacecraft, Symmetry, Vol. 14, 2022. 10.3390/sym14122589V.V. Lyubimov, Method of an Analysis of the Nonlinear Monotonic Simultaneous Stability of Two Orientation Angles of an Asymmetric Spacecraft in the Martian Atmosphere, Symmetry, Vol. 14, 2022. 10.3390/math11143142V.V. Lyubimov, A Method of Qualitative Analysis of the Monotonic Stability Region of Symmetric Particular Solutions of a Differential Equation, Mathematics, Vol. 11, 2023. G. A. Klekovkin, Spatial spirals, Mathematical education, Vol. 2, 2019.