TY - JOUR

T1 - Singular point analysis for dynamical systems with many parameters‐an application to an asymmetrically and densely connected neural network model

AU - Tanaka, Hisa‐Aki ‐A

AU - Okada, Atsushi

AU - Horiuchi, Kazuo

AU - Oishi, Shin'Ichi

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

KW - Singular point analysis

KW - high dimensional dynamical system

KW - nonlinear dynamical network

KW - self‐validating numerics

UR - http://www.scopus.com/inward/record.url?scp=84985822307&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84985822307&partnerID=8YFLogxK

U2 - 10.1002/ecjc.4430771009

DO - 10.1002/ecjc.4430771009

M3 - Article

AN - SCOPUS:84985822307

VL - 77

SP - 92

EP - 102

JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

SN - 1042-0967

IS - 10

ER -