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Algorithmic Detection of Jacobi Stability for Systems of Second Order Differential Equations Jacobi Stability of Systems of Second Order ODEs

  • Christian Boehmer
  • , Bo Huang*
  • , Dongming Wang
  • , Xinyu Wang
  • *Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This paper introduces an algorithmic approach to the analysis of Jacobi stability of systems of second order ordinary differential equations (ODEs) via the Kosambi Cartan Chern (KCC) theory. We develop an efficient symbolic program using Maple for computing the second KCC invariant for systems of second order ODEs in arbitrary dimension. The program allows us to systematically analyze Jacobi stability of a system of second order ODEs by means of real solving and solution classification using symbolic computation. The effectiveness of the proposed approach is illustrated by a model of wound strings, a two-dimensional airfoil model with cubic nonlinearity in supersonic flow and a 3-DOF tractor seat-operator model. The computational results on Jacobi stability of these models are further verified by numerical simulations. Moreover, our algorithmic approach allows us to detect hand-guided computation errors in published papers.

Original languageEnglish
Title of host publicationISSAC 2025 - Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation
EditorsCarlos D'Andrea, Sonia Perez Diaz, Santiago Laplagne
PublisherAssociation for Computing Machinery, Inc
Pages114-122
Number of pages9
ISBN (Electronic)9798400720758
DOIs
StatePublished - 10 Nov 2025
Event50th International Symposium on Symbolic and Algebraic Computation, ISSAC 2025 - Guanajuato, Mexico
Duration: 28 Jul 20251 Aug 2025

Publication series

NameISSAC 2025 - Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation

Conference

Conference50th International Symposium on Symbolic and Algebraic Computation, ISSAC 2025
Country/TerritoryMexico
CityGuanajuato
Period28/07/251/08/25

Keywords

  • Algorithmic approach
  • Jacobi stability
  • KCC theory
  • differential equations
  • semi-algebraic system
  • symbolic computation

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