Zero-Hopf bifurcation for a class of Lorenz-type systems

DOI10.3934/dcdsb.2014.19.1731zbMath1351.37207OpenAlexW2326363853MaRDI QIDQ478665

Jaume Llibre, Ernesto Pérez-Chavela

Publication date: 4 December 2014

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2014.19.1731

zbMATH Keywords

limit cyclesLorenz-type systemthree-dimensional differential systemszero-Hopf equilibrium

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Averaging method for ordinary differential equations (34C29) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

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Cites Work

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• Hopf bifurcation for some analytic differential systems in \(\mathbb R^3\) via averaging theory
• Converting a general 3-D autonomous quadratic system to an extended Lorenz-type system
• Hopf bifurcation in higher dimensional differential systems via the averaging method
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Averaging methods for finding periodic orbits via Brouwer degree.
• Limit cycles of the generalized polynomial Liénard differential equations
• Averaging methods in nonlinear dynamical systems
• Elements of applied bifurcation theory

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