多噪声源可激系统中的激活过程：一个和两个相互作用单元
Activation process in excitable systems with multiple noise sources: One and two interacting units
摘要：
我们考虑两个不同的噪声源的共同作用的激活过程中的一个单一的和两个相互作用的可激发单元，这是数学描述的Fitzhugh-Nagumo方程。我们确定最有可能的激活路径周围的相应的随机轨迹聚类。关键点在于引入适当的边界条件，是相关的第二类可激单元，这可以立即推广到涉及两个耦合单元的情况。我们分析了两个噪声源对激活过程的统计特征的影响，特别是演示了这些是如何由于线性/非线性形式的相互作用而被修改的。的激活过程的普遍性质定性地讨论了随机分岔的基础上从一个随机稳定的不动点连续振荡的过渡。
英文摘要：
We consider the coaction of two distinct noise sources on the activation process of a single and two interacting excitable units, which are mathematically described by the Fitzhugh-Nagumo equations. We determine the most probable activation paths around which the corresponding stochastic trajectories are clustered. The key point lies in introducing appropriate boundary conditions that are relevant for a class II excitable unit, which can be immediately generalized also to scenarios involving two coupled units. We analyze the effects of the two noise sources on the statistical features of the activation process, in particular demonstrating how these are modified due to the linear/nonlinear form of interactions. Universal properties of the activation process are qualitatively discussed in the light of a stochastic bifurcation that underlies the transition from a stochastically stable fixed point to continuous oscillations.
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