Coherence resonance for time-averaged measures

Go Uchida

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arXiv · 2308.09342

Coherence resonance for time-averaged measures

Go Uchida

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Abstract

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.

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Go Uchida. 2023-08-18. Coherence resonance for time-averaged measures. https://arxiv.org/abs/2308.09342

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