标题： Hindmarsh-Rose模型中外共存区域的随机双节律性 显示英文标题

标题： Stochastic birhythmicity outside the coexistence region in the Hindmarsh-Rose model

摘要： 在这项工作中，我们证明了受到加性白噪声影响的Hindmarsh-Rose模型表现出双节律性。具体而言，系统在两种不同的爆发吸引子之间波动，这些吸引子由不同数量的尖峰特征化。这种行为不仅出现在由两个极限环的鞍结分岔限定的双稳态区域内，而且超出了这些边界。这一现象与鬼影效应有关，通常在确定性的鞍结分岔附近观察到。我们根据噪声强度和控制快离子通道动力学的关键确定性参数来映射随机双节律性区域。为了提供分析基础，我们引入了一个具有单一鞍结分岔的简单随机模型。在这个模型中，随机双节律性同样被描述为噪声强度和控制参数的函数。 显示英文摘要

摘要： In this work, we demonstrate that the Hindmarsh-Rose model subjected to additive white noise exhibits birhythmicity. Specifically, the system fluctuates between two distinct bursting attractors characterized by different numbers of spikes. This behavior is observed not only within the bistable region bounded by two saddle-node bifurcations of limit cycles but also beyond these boundaries. This phenomenon is associated with the ghost effect, typically observed near deterministic saddle-node bifurcations. We map the region of stochastic birhythmicity in terms of the noise intensity and a key deterministic parameter that controls the dynamics of fast ion channels. To provide an analytical foundation, we introduce a simple stochastic model with a single saddle-node bifurcation. In this model, stochastic birhythmicity is similarly characterized as a function of noise intensity and the control parameter.