SINGULAR POINT ANALYSIS FOR DYNAMICAL-SYSTEMS WITH MANY PARAMETERS - AN APPLICATION TO AN ASYMMETRICALLY AND DENSELY CONNECTED NEURAL-NETWORK MODEL

In the nonlinear dynamical system, the singular point analysis (Painle ve test) is known to be an analytic method for identifying integrable systems or characterizing chaos. In this paper, nonlinear dynamical ne tworks, which are simplified models for mutually connected analog neur ons, are studied mainly in terms of the singular point analysis by int roducing the complex time. The following results were obtained: 1) som e conditions for integrability and first integrals are identified; 2) as an application of Yoshida's theorem, it is proven that many cases i n our system are (algebraically) noninegrable; 3) a self-validated num erical algorithm is proposed to overcome some difficulties known to ap pear in applying the singular point analysis (Yoshida's theorem) to hi gher-order systems.