徳島大学 教育・研究者情報データベース(EDB)

1. 徳島大学.医学部.保健学科.放射線技術科学専攻.診療放射線技術学講座

1. 吉永 哲哉([徳島大学.大学院医歯薬学研究部.保健学域.保健科学部門.放射線科学系.医用画像機器工学])

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(英) Bifurcation analysis of synaptically coupled neuronal model

(日) シナプス結合ニューロンモデルの分岐解析

(英) We investigate bifurcations of periodic solutions in model equations of neurons coupled through the characteristics of synaptic transmissions with a time delay. The model can be considered as a dynamical system whose solution includes jumps depending on a condition related to the behavior of the trajectory. Although the solution is discontinuous, we can define the Poincare map as a synthesis of successive submaps, and give its derivatives for obtaining periodic points and their bifurcations.Using our proposed method, we clarify mechanisms of bifurcations among synchronized oscillations with phase-locking patterns by analyzing periodic solutions observed in a model of coupled Hodgkin-Huxley equations. Moreover we illustrate a mechanism of the generation of chaotic itinerancy or the phenomenon of chaotic transitions among several quasi-stable states, which corresponds to associative dynamics or memory searching process in real neurons, by the analysis of four-coupled Bonhoffer-van der Pol equations.

1. (英) coupled neuron model
2. (英) synaptic transmission
3. (英) bifurcation
4. (英) nonlinear dynamical system