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ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

Stability Analysis and Inverse Matrix Projective Anti-synchronization of Chaotic Systems

Journal of Vibration Testing and System Dynamics 10(3) (2026) 247--258 | DOI:10.5890/JVTSD.2026.09.003

Vijay K. Shukla$^{1}$, Timur N. Mokaev$^{2}$, Arun K. Pandey$^{1}$

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

$^{2}$ Faculty of Mathematics and Mechanics, St. Petersburg University, St. Petersburg, Russia

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Abstract

This paper investigates the stability and synchronization of Li system by combining Jacobi stability analysis within the Kosambi–Cartan–Chern (KCC) framework and inverse matrix projective anti-synchronization (IMPAS) scheme. First, we extend Jacobi stability criteria to a broad class of nonlinear dynamical systems and derive general conditions that complement conventional Lyapunov analysis. Second, we propose an IMPAS controller that simplifies the synchronization of chaotic systems through an arbitrary scaling matrix. Numerical simulations confirm the theoretical predictions and illustrate the practical effectiveness of the method. The results deepen our geometric understanding of stability and broaden the tool for controlling real-world nonlinear systems.

Acknowledgments

The second author [Timur N. Mokaev] is supported by the RSF Project 25-11-00147.

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