Noise can induce time order in the dynamics of nonlinear dynamical systems. For example, coherence resonance occurs in various neuron models driven by a noise. In studies of coherence resonance, ensemble-averaged measures of the coherence are often used. In the present study, we examine coherence resonance for time-averaged measures. For the examination, we use a Hodgkin-Huxley neuron model driven by a constant current and a noise. We firstly show that for large times, the neuron is in a stationary state irrespective of initial conditions of the neuron. We then show numerical evidence that in the stationary state, a given noise sample path uniquely determines the dynamics of the neuron. We then present numerical evidence suggesting that time-averaged coherence measures of the dynamics is independent of noise sample paths and is equal to ensemble-averaged coherence measures. On the basis of this property, we show that coherence resonance is not only a phenomenon related to ensemble-averaged measures but also a phenomenon that holds for time-averaged measures.
No persistent circadian oscillator at genome resolution: pseudo-coherence in gut microbiome dynamics
Institute of Risks Analysis, Prediction and Management, Southern University of Science and Technology（南方科技大学风险分析与预测管理研究所）；Meinig School of Biomedical Engineering, Cornell University（康奈尔大学梅尼格生物医学工程学院）；Graduate School of Informatics, Nagoya University（名古屋大学情报学研究科）；RIKEN Center for Integrative Medical Sciences（理化学研究所综合医学科学中心）；Department of Computer Science, Institute of Science Tokyo（东京科学大学计算机科学系）
