Zaks M A, Sailer X, Schimansky-Geier L, Neiman A B
Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, D-12489 Berlin, Germany.
Chaos. 2005 Jun;15(2):26117. doi: 10.1063/1.1886386.
We study the stochastic dynamics of an ensemble of N globally coupled excitable elements. Each element is modeled by a FitzHugh-Nagumo oscillator and is disturbed by independent Gaussian noise. In simulations of the Langevin dynamics we characterize the collective behavior of the ensemble in terms of its mean field and show that with the increase of noise the mean field displays a transition from a steady equilibrium to global oscillations and then, for sufficiently large noise, back to another equilibrium. In the course of this transition diverse regimes of collective dynamics ranging from periodic subthreshold oscillations to large-amplitude oscillations and chaos are observed. In order to understand the details and mechanisms of these noise-induced dynamics we consider the thermodynamic limit N-->infinity of the ensemble, and derive the cumulant expansion describing temporal evolution of the mean field fluctuations. In Gaussian approximation this allows us to perform the bifurcation analysis; its results are in good qualitative agreement with dynamical scenarios observed in the stochastic simulations of large ensembles.
我们研究了由N个全局耦合的可激发元件组成的集合的随机动力学。每个元件由一个菲茨休 - 纳古莫振荡器建模，并受到独立高斯噪声的干扰。在朗之万动力学模拟中，我们根据平均场来表征集合的集体行为，并表明随着噪声的增加，平均场呈现出从稳定平衡到全局振荡的转变，然后，对于足够大的噪声，又回到另一个平衡。在这个转变过程中，观察到了从周期性亚阈值振荡到大幅度振荡和混沌等各种集体动力学状态。为了理解这些噪声诱导动力学的细节和机制，我们考虑集合的热力学极限N→∞，并推导描述平均场涨落时间演化的累积量展开式。在高斯近似下，这使我们能够进行分岔分析；其结果与大型集合的随机模拟中观察到的动力学情况在定性上有很好的一致性。
