Persistence of the Hopf Bifurcation under Singular Perturbations

机译：奇异摄动下Hopf分支的持续性

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The purpose of this paper is to study persistence of the Hopf bifurcation under singular perturbations of the associated vector field. Both single parameter and multiparameter singular perturbation problems are considered. In each case, hyperbolicity of an associated fast time system is shown to imply persistence. For single parameter singular perturbation problems, we employ Fenichel's center manifold theorem for singularly perturbed systems (1) to prove regular degeneration of the bifurcated periodic solutions and to study their stability. (ERA citation 09:033016)

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作者
Abed, E. H.;
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年度 1984
页码 1-8
总页数 8
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Power Systems; Disturbances; Mathematics; Parametric Analysis;

机译：电力系统;干扰;数学;参数分析;

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2. Hopf bifurcations in multiple-parameter space of the Hodgkin-Huxley equations II. Singularity theoretic approach and highly degenerate bifurcations [J] . Fukai H., Doi S., Sato S., Biological Cybernetics: Communication and Control in Organisms and Automata: = Nachrichtenubertragung, Nachrichtenverarbeitung, Steuerung und Regelung in Organismen und in Automaten . 2000,第3期

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3. Uniform persistence and Hopf bifurcations in ?_+~n [J] . Antonio Giraldo, Víctor F. Laguna, José M.R. Sanjurjo Journal of Differential Equations . 2014,第8期

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Persistence of the Hopf Bifurcation under Singular Perturbations

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