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Selforganizology, 2023, 10(3-4): 7-21
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Article

A new chaotic system's qualitative analysis, with a focus on Hopf bifurcation analysis

Md. Jasim Uddin, Esrat Nur Nipu
University of Dhaka, Department of Mathematics, Dhaka-1000, Dhaka, Bangladesh

Received 22 November 2022;Accepted 31 December 2022;Published online 20 January 2022;Published 1 December 2023
IAEES

Abstract
In this study, a brand-new chaotic system with a particular set of parameters is presented. In addition, this study offers instructions about how to resolve the new system. Also demonstrated and stated are some of the system's dynamical characteristics. In essence, this work demonstrates the identification of the fixed points for the system, dynamical analysis utilizing the complementary-cluster energy-barrier criteria (CCEBC), eigenvalue discovery for stability, and Lyapunov exponent discovery to examine some of the dynamical behaviors of the system. Additionally, this research uses the first Lyapunov coefficient to determine the Hopf bifurcation of the new three-dimensional system. With the help of MATLAB, many parameters are changed to display images and diagrams for chaotic systems.

Keywords Hopf bifurcation;Lyapunov exponent;first Lyapunov coefficient;Routh-Hurwitz Criterion.

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