To study the effect of electromagnetic induction on the electric activities of neuron, memristive neuron models have been proposed by coupling membrane potential with magnetic flux. In this paper, on the basis of memristive Hindmarsh-Rose neuron model, time-delay memristive Hindmarsh-Rose neuron model is described and the responses of neuron in electrical activities are detected. The effect of time-delay on the dynamical behaviors of the neuron is discussed and the transition of electrical activities of the neuron is investigated with the change of noise intensity. It is found that, both the time-delay and the noise have effect on the electrical activities of the neuron. Especially, by selecting appropriate parameters, the noise not only can excite neuron from quiescent state to bursting state, but also can suppress the electrical activities in neuron during certain discharge period. Results mean that multiple modes and coherence resonance can be observed by changing the size of time-delay or the noise intensity, which could be associated with memory effect and self-adaption in neurons.

中文翻译：

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高斯白噪声干扰的时滞忆阻性神经元的电活动

为了研究电磁感应对神经元电活动的影响，通过将膜电位与磁通量耦合，提出了忆阻性神经元模型。本文在忆阻性Hindmarsh-Rose神经元模型的基础上，描述了时滞忆阻性Hindmarsh-Rose神经元模型，并检测了神经元在电活动中的反应。讨论了时延对神经元动力学行为的影响，并研究了噪声强度变化对神经元电活动的影响。发现，时间延迟和噪声都对神经元的电活动有影响。特别是通过选择合适的参数，噪声不仅可以使神经元从静止状态激发到爆发状态，而且还可以抑制某些放电期间神经元的电活动。结果表明，通过改变时延的大小或噪声强度，可以观察到多种模式和相干共振，这可能与神经元的记忆效应和自适应有关。