Qualitative analysis on Fitzhugh's nerve conduction equation
type: Item
instance of: scholarly article
title: Qualitative analysis on Fitzhugh's nerve conduction equation
zbMATH Open document ID: 0619.34035
author: Suilin Cai
author: Pingguang Zhang
published in: Chinese Annals of Mathematics. Series B
publication date: 1986-01-01T00:00:00Z
review text: This paper brings to light a number of new facts in the qualitative analysis of the simplified FitzHugh nerve conduction equation. The emphasis is put here on the existence and the number of periodic solutions, depending on parameters. Results indicate uniqueness as well as non-uniqueness and non-existence on a range of parameters, leaving few places undetermined. The method is based on a careful and fine analysis carried out through the use of some of the various tools currently available in the study of qualitative properties of ordinary differential equations: the Poincaré-Bendixson theorem, the computation of focal values, Filippov's transformation and also some which seem to have been developed (or improved from earlier versions) by Chinese mathematicians. This paper appears at the same time as a recent translation of a book by \textit{Yeh Yan-Qian}, et al. (including \textit{Cai Suilin}) entitled ''Theory of limit cycles'' (1986; Zbl 0588.34022). And, in fact, it is not an exaggeration to write that the paper is mainly an illustration of the effectiveness of the techniques detailed in the book. (This paper is also a combination of two papers published (in Chinese) separately by each of the authors.)
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 4004662
zbMATH Keywords: limit cycle
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: focal values
zbMATH Keywords: Dulac condition
zbMATH Keywords: FitzHugh nerve conduction equation
zbMATH Keywords: Poincaré-Bendixson theorem
zbMATH Keywords: computation of focal values
zbMATH Keywords: Filippov's transformation
reviewed by: Ovide Arino
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4004662