Qualitative analysis on Fitzhugh's nerve conduction equation
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.)
scientific article; zbMATH DE number 4004662