A new three-dimensional (3D) memristive HR neuron model is presented, which is improved from an existing memristive HR neuron model using a memristor synapse with sine memductance to substitute the original one. The improved memristive HR neuron model has no equilibrium but hidden firing activities can emerge with discrete memristor initial-offset boosting. Treating the neuron model as a two-dimensional (2D) major subsystem controlled by a magnetic flux variable, fold bifurcations for hidden chaotic and periodic firing patterns are elaborated. The coexistence of hidden firing patterns induced by memristor initial boosting is quantitatively analyzed and numerically simulated by bifurcation plots, phase plots, and basins of attraction. The results demonstrate that the improved memristive HR neuron model can exhibit a discrete memristor initial-offset boosting behavior owning infinitely many disconnected basins of attraction and the generating firing patterns can be boosted to different discrete levels by changing the memristor initial value, differing entirely from various boosting behaviors reported previously. Therefore, infinitely many hidden coexisting offset-boosted firing patterns with the same initial-offsets and attractor types are disclosed along the boosting route, which are homogenous with extreme multistability and are perfectly validated by PSIM circuit simulations based on a physically implementation-oriented analog circuit.

中文翻译：

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具有隐藏触发模式的忆阻 HR 神经元模型中的忆阻器初始偏移提升

提出了一种新的 3D (3D) 忆阻 HR 神经元模型，它是从现有的忆阻 HR 神经元模型改进而来，使用具有正弦电感的忆阻器突触替代原始模型。改进的忆阻 HR 神经元模型没有平衡，但随着离散忆阻器初始偏移提升，可能会出现隐藏的放电活动。将神经元模型视为由磁通量变量控制的二维 (2D) 主要子系统，详细阐述了隐藏混沌和周期性发射模式的折叠分叉。通过分叉图、相位图和吸引力盆地对忆阻器初始升压引起的隐藏发射模式的共存进行了定量分析和数值模拟。结果表明，改进的忆阻 HR 神经元模型可以表现出离散忆阻器初始偏移增强行为，该行为具有无限多个不连贯的吸引力盆地，并且可以通过改变忆阻器初始值将产生的放电模式提升到不同的离散水平，这完全不同于各种之前报道的助推行为。因此，在提升路径上揭示了无限多隐藏的共存偏移提升激发模式，它们具有相同的初始偏移和吸引子类型，它们是同质的，具有极高的多稳定性，并且通过基于面向物理实现的模拟电路的 PSIM 电路模拟得到完美验证.