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
SN - 1042-0967
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)
IS - 10
ER -