Hopf Bifurcation and Chaotic Attractors in Two Special Jerk System Cases

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science,Soran University,Soran, Kurdistan Region, Iraq.

2 Department of Mathematics, College of Basic Education,University of Raparin, Rania, Kurdistan Region, Iraq.

Abstract

This paper is focused on studying the Hopf bifurcation with self-excited and hidden chaotic attractors in special types of chaotic jerk systems. The stability of the equilibrium point and Hopf bifurcation is rigorously investigated for the proposed systems. It is remarkable to analyze the Hopf bifurcation using focus quantity techniques. These bifurcations may be either supercritical or subcritical, depending on the control parameters. To investigate the dynamic behavior of the systems, an analysis of self-excited chaotic attractors and hidden chaotic attractors was performed. Additionally, bifurcation analysis and evaluation of Lyapunov exponents revealed complex transitions among periodic, self-excited chaotic and hidden chaotic attractors as the system parameters varied. It was found that the systems exhibit both self-excited and hidden attractors, as demonstrated by the bifurcation diagrams, Lyapunov exponents and cross sections. All of the results provided in this study were acquired applying the Maple and Matlab software.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 15 January 2025

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History

  • Receive Date: 29 May 2024
  • Revise Date: 25 November 2024
  • Accept Date: 12 January 2025

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