シナプス結合ニューロンモデルの分岐解析

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  • シナプス ケツゴウ ニューロン モデル ノ ブンキ カイセキ
  • Bifurcation analysis of synaptically coupled neuronal model

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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.

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