Study of the Hopf bifurcation in the Lorenz, Chen and Lü systems

DOI10.1007/s11071-014-1709-2zbMath1345.34069OpenAlexW2073702678MaRDI QIDQ493922

María C. Domínguez-Moreno, Antonio Algaba, Alejandro J. Rodríguez-Luis, Manuel Merino

Publication date: 7 September 2015

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-014-1709-2

zbMATH Keywords

Hopf bifurcationLorenz equationsdegeneracyChen systemLü systemcodimension-three bifurcationcusp bifurcation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Bifurcations of singular points in dynamical systems (37G10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28)

Related Items (12)

On differences and similarities in the analysis of Lorenz, Chen, and Lu systems ⋮ Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system ⋮ Local bifurcation and center problem for a more generalized Lorenz system ⋮ Bifurcation of limit cycles and isochronous centers on center manifolds for a class of cubic Kolmogorov systems in \(\mathbb{R}^3\) ⋮ Takens-Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system ⋮ Dynamical transition and chaos for a five‐dimensional Lorenz model ⋮ Superluminal periodic orbits in the Lorenz system ⋮ Analysis of the T-point-Hopf bifurcation in the Lorenz system ⋮ Study of a simple 3D quadratic system with homoclinic flip bifurcations of inward twist case \(\mathbf{C}_{\mathbf{in}}\) ⋮ Center cyclicity of Lorenz, Chen and Lü systems ⋮ Unstable periodic orbits analysis in the generalized Lorenz-type system ⋮ Retardational Effect and Hopf Bifurcations in a New Attitude System of Quad-Rotor Unmanned Aerial Vehicle

Uses Software

• AUTO
• AUTO-07P
• HomCont

Cites Work

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