Franović Igor, Todorović Kristina, Vasović Nebojša, Burić Nikola
Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, 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. 2014 Feb;89(2):022926. doi: 10.1103/PhysRevE.89.022926. Epub 2014 Feb 28.
We consider the approximations behind the typical mean-field model derived for a class of systems made up of type II excitable units influenced by noise and coupling delays. The formulation of the two approximations, referred to as the Gaussian and the quasi-independence approximation, as well as the fashion in which their validity is verified, are adapted to reflect the essential properties of the underlying system. It is demonstrated that the failure of the mean-field model associated with the breakdown of the quasi-independence approximation can be predicted by the noise-induced bistability in the dynamics of the mean-field system. As for the Gaussian approximation, its violation is related to the increase of noise intensity, but the actual condition for failure can be cast in qualitative, rather than quantitative terms. We also discuss how the fulfillment of the mean-field approximations affects the statistics of the first return times for the local and global variables, further exploring the link between the fulfillment of the quasi-independence approximation and certain forms of synchronization between the individual units.
我们考虑了为一类由受噪声和耦合延迟影响的II型可激发单元组成的系统推导的典型平均场模型背后的近似。这两种近似的表述，即高斯近似和准独立近似，以及验证其有效性的方式，都经过调整以反映基础系统的基本特性。结果表明，与准独立近似失效相关的平均场模型的失效可以通过平均场系统动力学中的噪声诱导双稳性来预测。至于高斯近似，其失效与噪声强度的增加有关，但实际的失效条件可以用定性而非定量的术语来描述。我们还讨论了平均场近似的满足如何影响局部和全局变量首次返回时间的统计，进一步探索准独立近似的满足与单个单元之间某些同步形式之间的联系。
