アドホックネットワーク，ユビキタス・ネットワーク

同期現象（シンクロニゼーション）の解明，同期システムへの応用

ネットワークダイナミクス, 粘菌の分散知能の研究

筋肉のHodgkin-Huxley方程式の2パラメータ分岐

田中 久陽，寺田 和子，吉澤 修治
電子情報通信学会論文誌 A, vol. J81-A, No. 10, pp. 1331-1338, 1998年10月

Abstract

カエル骨格筋のHodgkin-Huxley方程式(HHM)において, 筋緊張症と周期性四肢麻痺が生じる機序を示すことを目的として, これらイオンチャネル疾患にかかわる生理特性値であるリークコンダクタンスglとNaチャネルに関連するVmとをパラメータとした分岐現象を, 数値計算によって調べた. glとVmの空間上で, 余次元1の分岐であるsaddle node分岐, homoclinic分岐, Hopf分岐, double cycle分岐曲線を追跡し, 余次元2の分岐であるtwisted resonant, Bogdanov-Takens, inclination-flip(if), degenerate Hopf, cusp点を見出した.生理的に意味のあるglが正値の範囲において, 膜の静止状態にあるときに通常の刺激入力が入った場合のHHMの振舞いは, if点を3さ(叉)点とする3領域で異なっており, 1回のみの発火, 周期的発火, 脱分極電位へ収束の3種であった.これらは, それぞれ, 正常な状態, 筋緊張症, 周期性四肢麻痺に対応すると考えられる.if点周辺の分岐は, 理論的にも完全には明らかにされておらず, 数理的にも興味深い.

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