@inproceedings{491b08a42af1444fae2584eec414ad23,
title = "Algorithmic Detection of Jacobi Stability for Systems of Second Order Differential Equations Jacobi Stability of Systems of Second Order ODEs",
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.",
keywords = "Algorithmic approach, Jacobi stability, KCC theory, differential equations, semi-algebraic system, symbolic computation",
author = "Christian Boehmer and Bo Huang and Dongming Wang and Xinyu Wang",
note = "Publisher Copyright: {\textcopyright} 2025 Copyright held by the owner/author(s).; 50th International Symposium on Symbolic and Algebraic Computation, ISSAC 2025 ; Conference date: 28-07-2025 Through 01-08-2025",
year = "2025",
month = nov,
day = "10",
doi = "10.1145/3747199.3747553",
language = "英语",
series = "ISSAC 2025 - Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation",
publisher = "Association for Computing Machinery, Inc",
pages = "114--122",
editor = "Carlos D'Andrea and Diaz, \{Sonia Perez\} and Santiago Laplagne",
booktitle = "ISSAC 2025 - Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation",
}