Boehmer, Christian;
Huang, Bo;
Wang, Dongming;
Wang, Xinyu;
(2025)
Algorithmic Detection of Jacobi Stability for Systems of Second Order Differential Equations.
In:
ISSAC '25: Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation.
(pp. pp. 114-122).
ACM
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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.
| Type: | Proceedings paper |
|---|---|
| Title: | Algorithmic Detection of Jacobi Stability for Systems of Second Order Differential Equations |
| Event: | ISSAC '25: International Symposium on Symbolic and Algebraic Computation |
| ISBN-13: | 9798400720758 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1145/3747199.3747553 |
| Publisher version: | https://doi.org/10.1145/3747199.3747553 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10217979 |
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