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- Title
Hopf and Zero-Hopf Bifurcation Analysis for a Chaotic System.
- Authors
Husien, Ahmad Muhamad; Amen, Azad Ibrahim
- Abstract
In this paper, we investigate a quadratic chaotic system modeling self-excited and hidden attractors which is described by a system of three nonlinear ordinary differential equations with three real parameters. The primary goal is to establish the existence of two limit cycles that bifurcate based on the system's nature as an electronic circuits model, specifically via Hopf bifurcation. Notably, the application of the first and second Lyapunov coefficients is utilized to demonstrate the bifurcation of two limit cycles from an equilibrium point near a Hopf critical point. Furthermore, employing the first-order averaging theory enables us to confirm the presence of unstable periodic orbits originating from the zero-Hopf equilibrium.
- Subjects
HOPF bifurcations; LIMIT cycles; ORDINARY differential equations; NONLINEAR differential equations; ELECTRONIC circuits; ORBITS (Astronomy)
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2024, Vol 34, Issue 8, p1
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127424501049