The k-Zero Bifurcation Theorem for m-Parameterized Systems

DOI10.1142/S0218127418501006zbMath1397.34066OpenAlexW2887877716WikidataQ129395116 ScholiaQ129395116MaRDI QIDQ4583277

Francisco A. Carrillo, Martin A. Carrillo, Fernando Verduzco

Publication date: 28 August 2018

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127418501006

zbMATH Keywords

center manifold theoryunfolding\(k\)-zero 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) Invariant manifolds for ordinary differential equations (34C45)

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Versal deformation of a singular point of a vector field on the plane in the case of zero eigenvalues
• Bifurcations of planar vector fields. Nilpotent singularities and Abelian integrals
• Asymptotic unfoldings of dynamical systems by normalizing beyond the normal form
• Nilpotent singularities in generic 4-parameter families of 3-dimensional vector fields
• An equation for continuous chaos
• New aspects in the unfolding of the nilpotent singularity of codimension three
• ANALYSIS OF THE TAKENS–BOGDANOV BIFURCATION ON m-PARAMETERIZED VECTOR FIELDS
• Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3
• Singularities of vector fields on
• A NOTE ON THE TRIPLE-ZERO LINEAR DEGENERACY: NORMAL FORMS, DYNAMICAL AND BIFURCATION BEHAVIORS OF AN UNFOLDING
• PRACTICAL COMPUTATION OF NORMAL FORMS ON CENTER MANIFOLDS AT DEGENERATE BOGDANOV–TAKENS BIFURCATIONS

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