Nonintegrability of the unfoldings of codimension-two bifurcations

2020/02/13 by Primitivo B. Acosta-Humánez, Primitivo B Acosta-Humánez, Kazuyuki Yagasaki · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · doi:10.1088/1361-6544/ab60d4

openalex created_date 2019/04/11 · openalex publication_date 2020/02/13 · openalex updated_date 2026/07/30

Abstract

Abstract Codimension-two bifurcations are fundamental and interesting phenomena in dynamical systems. Fold-Hopf and double-Hopf bifurcations are the most important among them. We study the unfoldings of these two codimension-two bifurcations, and obtain sufficient conditions for their nonintegrability in the meaning of Bogoyavlenskij. We reduce the problems of the unfoldings to those of planar polynomial vector fields and analyze the nonintegrability of the planar vector fields, based on Ayoul and Zung’s version of the Morales–Ramis theory. New useful criteria for nonintegrability of planar polynomial vector fields are also obtained. The approaches used here are applicable to many problems including circular symmetric systems.

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• Transcritical Bifurcations and Algebraic Aspects of Quadratic\n Multiparametric Families
• Integrability and dynamics of the Poisson–Boltzmann equation in simple geometries

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