Rigorous verification of saddle-node bifurcations in ODEs

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• 作者：Jean-Philippe Lessard ^{jean-philippe.lessard@mat.ulaval.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Saddle&ndash ; node bifurcation ; Rigorously verified numerics ; Contraction mapping theorem ; Hodgkin&ndash ; Huxley model
• 刊名：Indagationes Mathematicae
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：27
• 期：4
• 页码：1013-1026
• 全文大小：276 K

文摘

In this paper, we introduce a general method for the rigorous verification of saddle–node bifurcations in ordinary differential equations. The approach is constructive in the sense that we obtain precise and explicit bounds within which the saddle–node bifurcation occurs. After introducing a set of sufficient generic conditions, an algorithm to verify rigorously the conditions is introduced. The approach is applied to prove existence of saddle–node bifurcations in the Hodgkin–Huxley model.