In the nonlinear dynamical system, the singular point analysis (Painleve test) is known to be an analytic method for identifying integrable systems or characterizing chaos. In this paper, nonlinear dynamical networks, which are simplified models for mutually connected analog neurons, are studied mainly in terms of the singular point analysis by introducing the complex time. The following results were obtained: 1) some conditions for integrability and first integrals are identified; 2) as an application of Yoshida's theorem, it is proven that many cases in our system are (algebraically) noninegrable; 3) a self‐validated numerical algorithm is proposed to overcome some difficulties known to appear in applying the singular point analysis (Yoshida's theorem) to higher‐order systems.
|ジャーナル||Electronics and Communications in Japan (Part III: Fundamental Electronic Science)|
|出版ステータス||Published - 1994|
ASJC Scopus subject areas