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Discontinuity, Nonlinearity, and Complexity 13(2) (2024) 311--321 | DOI:10.5890/DNC.2024.06.009

Vijay K. Shukla$^{1}$, Vijay K. Yadav$^{2}$, Abhishek Kumar$^{3}$, Prashant K. Mishra$^{4}$

$^{1}$ Department of Mathematics, Shiv Harsh Kisan P.G. College, Basti-272001, India

$^{2}$ Department of Mathematics, Amity University, Gurugram-122413, India

$^{3}$ Department of Mathematics, Jai Prakash University, Chapra-841301, India

$^{4}$ Department of Mathematics, P. C. Vigyan Mahavidyalaya, Jai Prakash University, Chapra-841301, India

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Abstract

This article investigates Jacobi stability analysis of unified chaotic system. The stability analysis of unified system has been discussed by using the Kosambi-Cartan-Chern (KCC) theory, which is based on differential geometry. The unified system is transformed into a pair of second-order differential equations. The five KCC invariants are obtained to study the dynamics of unified chaotic system. The deviation curvature tensor is obtained and it explains the stability of the system. Further, the dynamics of unified chaotic system near the equilibrium points is also discussed.

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