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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Jacobi and Linear Stability Analysis of T Chaotic System

Journal of Applied Nonlinear Dynamics 12(3) (2023) 523--536 | DOI:10.5890/JAND.2023.09.007

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, Nirma University, Ahmedabad-382481, 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

In this paper, the stability analysis of T chaotic system has been discussed by two different methods viz., Jacobi stability and linear stability methods. Jacobi stability analysis of T chaotic system has been studied by using geometro-dynamical approach with Kosambi-Cartan-Chern (KCC) theory. The deviation curvature tensor and five KCC invariants are obtained which express the intrinsic properties of nonlinear dynamical system. The dynamical behaviors of deviation vector components near the equilibrium points of T system are also discussed. The phase portrait of deviation vector components reflects the dynamical behavior of T system, which shows the instability and chaotic behaviour near the equilibrium points for a set of parameters.

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