Franović Igor, Perc Matjaž, Todorović Kristina, Kostić Srdjan, Burić Nikola
Scientific Computing Laboratory, Institute of Physics, University of Belgrade, P. O. Box 68, 11080 Beograd-Zemun, Serbia.
Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška Cesta 160, SI-2000 Maribor, Slovenia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062912. doi: 10.1103/PhysRevE.92.062912. Epub 2015 Dec 14.
We study the activation process in large assemblies of type II excitable units whose dynamics is influenced by two independent noise terms. The mean-field approach is applied to explicitly demonstrate that the assembly of excitable units can itself exhibit macroscopic excitable behavior. In order to facilitate the comparison between the excitable dynamics of a single unit and an assembly, we introduce three distinct formulations of the assembly activation event. Each formulation treats different aspects of the relevant phenomena, including the thresholdlike behavior and the role of coherence of individual spikes. Statistical properties of the assembly activation process, such as the mean time-to-first pulse and the associated coefficient of variation, are found to be qualitatively analogous for all three formulations, as well as to resemble the results for a single unit. These analogies are shown to derive from the fact that global variables undergo a stochastic bifurcation from the stochastically stable fixed point to continuous oscillations. Local activation processes are analyzed in the light of the competition between the noise-led and the relaxation-driven dynamics. We also briefly report on a system-size antiresonant effect displayed by the mean time-to-first pulse.
我们研究了II型可兴奋单元大集合中的激活过程，其动力学受两个独立噪声项的影响。应用平均场方法明确证明，可兴奋单元集合本身可表现出宏观可兴奋行为。为便于比较单个单元和集合的可兴奋动力学，我们引入了集合激活事件的三种不同表述。每种表述处理相关现象的不同方面，包括类阈值行为和单个尖峰相干性的作用。发现集合激活过程的统计特性，如首次脉冲平均时间和相关变异系数，对于所有三种表述在定性上是相似的，并且类似于单个单元的结果。这些相似性表明源于全局变量经历从随机稳定不动点到连续振荡的随机分岔这一事实。根据噪声主导和弛豫驱动动力学之间的竞争对局部激活过程进行了分析。我们还简要报告了首次脉冲平均时间所显示的系统规模反共振效应。
