Bifurcation of Inter-Spike-Interval Density of Piecewise-Constant Chaotic Spiking Oscillator with Dead-Time

摘要

In this report, we consider inter-spike-interval (abbr. ISI) density of a chaotic spiking oscillator (abbr. CSO) with piecewise-constant vector field. The CSOs exhibits chaotic behavior and generates various spike trains depends on its parameters. To study these spike trains is not only interesting for fundamental nonlinear problems, but also important for engineering applications. First, we show the ISI density shows various bifurcation phenomena depends on the parameters. And some theoretical results are also provided. Next, we introduce the dead-time controller to control the ISI density. The dead-time controller immobilizes the oscillation after the spike during some time depends on the state variable. We show the ISI density can be controlled by the dead-time in numerical simulations.%本稿では，区分的に定数なべクトル場を持つカオススパイキング発振器（CSO）のスパイク間隔分布（ISI）について議論を行う．CSOはカオス的振る舞いを呈しながら，多様なスパイク列を呈する．このスパイク列について考察を行うことは，基本的な非線形問題として興味深いだけでなく工学的にも重要である．本稿ではまず，不感時間制御機構を備えた区分定数スパイキング発振器を示し，パラメータに対するISI分布の変化を示すほか，ISI分布の理論的な解析を試みる．また，不惑時間を加えることでISI分布を変化させられることを数値シミュレーションから示す．