International Journal of Mathematics Trends and Technology
Volume 70 | Issue 10 | Year 2024 | Article Id. IJMTT-V70I10P104 | DOI : https://doi.org/10.14445/22315373/IJMTT-V70I10P104
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 11 Aug 2024 | 20 Sep 2024 | 11 Oct 2024 | 30 Oct 2024 |
KCC theory offers a robust geometric framework for analyzing the stability of dynamical systems described by second order differential equations. Its use of KCC invariants and Jacobi stability analysis provides insights into the behavior of nonlinear systems across various fields, including cosmology, mechanics, biology, and control theory. By transforming stability analysis into a geometric problem, the KCC theory enables a deeper understanding of the conditions under which systems maintain or lose stability, thereby offering practical insights into real-world applications. The main ideas of the KCC theory are examined in this study, along with how it is used for Jacobi stability analysis in specific systems. Jacobi stability for various dynamic systems, including the Rititake, Rossler, Chua circuit, RF, and tumor growth models, as well as the KCC theory and its constituent parts, is explained.
KCC- geometric theory, Jacobian stability, Deviation curvature tensor, Cartan tensor, Finsler connection.
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Nand Kishor Kumar, "Kosambi-Carton-Chern (KCC) Theory for Jacobi Stability Analysis in Certain Systems," International Journal of Mathematics Trends and Technology (IJMTT), vol. 70, no. 10, pp. 22-29, 2024. Crossref, https://doi.org/10.14445/22315373/IJMTT-V70I10P104
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