Franović Igor, Todorović Kristina, Perc Matjaž, Vasović Nebojša, Burić Nikola
Scientific Computing Laboratory, Institute of Physics, University of Belgrade, P. O. Box 68, 11080 Beograd-Zemun, Serbia.
Department of Physics and Mathematics, Faculty of Pharmacy, University of Belgrade, Vojvode Stepe 450, Belgrade, Serbia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062911. doi: 10.1103/PhysRevE.92.062911. Epub 2015 Dec 14.
We consider the coaction of two distinct noise sources on the activation process of a single excitable unit 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 or 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.
我们考虑两个不同噪声源对单个可兴奋单元以及两个相互作用的可兴奋单元激活过程的共同作用，这些过程由菲茨休 - 纳古莫方程进行数学描述。我们确定了相应随机轨迹聚集的最可能激活路径。关键在于引入与II类可兴奋单元相关的适当边界条件，该条件也可立即推广到涉及两个耦合单元的情形。我们分析了两个噪声源对激活过程统计特征的影响，特别展示了这些特征如何因线性或非线性相互作用形式而改变。根据从随机稳定不动点到连续振荡转变所基于的随机分岔，定性地讨论了激活过程的普遍性质。
