The equivalence between singular point quantities and Liapunov constants on center manifold

DOI10.1186/1687-1847-2012-78zbMath1294.34045OpenAlexW2141598965WikidataQ59289381 ScholiaQ59289381MaRDI QIDQ2448062

Wen-tao Huang, Qin-long Wang

Publication date: 29 April 2014

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2012-78

zbMATH Keywords

three-dimensional systemcenter manifoldsingular point quantitiesmultiple Hopf 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) Complex behavior and chaotic systems of ordinary differential equations (34C28) Invariant manifolds for ordinary differential equations (34C45)

Related Items (4)

Multiple limit cycles and centers on center manifolds for Lorenz system ⋮ Weak Bi-Center and Bifurcation of Critical Periods in a Three-Dimensional Symmetric Quadratic System ⋮ Bifurcation of limit cycles and isochronous centers on center manifolds for a class of cubic Kolmogorov systems in \(\mathbb{R}^3\) ⋮ Nine limit cycles around a weak focus in a class of three-dimensional cubic Kukles systems

Cites Work

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• Two limit cycles in three-dimensional Lotka-Volterra systems
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• A cubic system with twelve small amplitude limit cycles
• On the generalized Lorenz canonical form
• Hopf bifurcations in competitive three-dimensional Lotka–Volterra systems
• Evolutionary Games and Population Dynamics

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