University of Tabriz Computational Methods for Differential Equations 2345-3982 14 2 2026 04 01 Hopf bifurcation and chaotic attractors in two special jerk system cases 678 689 19141 10.22034/cmde.2024.61865.2694 EN Tahsin I Rasul Department of Mathematics, Faculty of Science, Soran University, Soran, Kurdistan Region, Iraq. Rizgar H. Salih Department of Mathematics, College of Basic Education, University of Raparin, Rania, Kurdistan Region, Iraq. Journal Article 2024 05 29 This paper investigates the Hopf bifurcation with self-excited and hidden chaotic attractors in special types of chaotic jerk systems. The stability of the equilibrium points and Hopf bifurcation are rigorously analyzed for the proposed systems. It is remarkable to analyze the Hopf bifurcation using focus quantity techniques. These bifurcations can be either supercritical or subcritical, depending on the control parameters. 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. https://cmde.tabrizu.ac.ir/article_19141_0d4a8898714d64a6c9d0c2f07b10128d.pdf