Pacemaker-driven stochastic resonance on diffusive and complex networks of bistable oscillators
Pacemaker-driven stochastic resonance on diffusive and complex networks of bistable oscillators
复制标题
DOI：
10.1088/1367-2630/10/5/053008
复制
发表时间：
2008-05
影响因子：
3.3
通讯作者：
M. Perc;M. Gosak
中科院分区：
文献类型：
--
作者：
M. Perc;M. Gosak
研究了由双稳过阻尼振子组成的小世界无标度扩散网络上的随机共振现象。因此，重要的是，外部亚阈值周期强迫仅被引入网络的单个振荡器。因此，强迫起到了起搏器的作用，试图通过被引入的单元将其节奏强加给整个网络。然而，在没有附加时空噪声的情况下，整个网络，包括直接接触起搏器的单元，永远陷于局部动力学的两个稳定稳态之一。结果表明，亚阈值起搏器活动的频率与网络响应之间的相关性与加性噪声的强度密切相关。已报道的起搏器驱动的随机共振最大程度地依赖于耦合强度和潜在的网络结构。也就是说，在最近邻相互作用的情况下，起搏器的外延遵循经典的扩散定律，因此与耦合强度的平方根成正比，而它通过适当的小世界或相互作用网络的无标度拓扑变得超扩散。特别是，无标度拓扑被认为是在整个网络中传播局部节律活动的最佳拓扑。此外，我们还证明了聚集系数和特征路径长度之间的比率是定义小世界网络促进起搏器发出的亚阈值节奏扩展的能力的关键数量。此外，我们还使用Fitzhugh-Nagumo可激发系统作为双稳过阻尼谐振子的替代方案来证实这些发现。
We study the phenomenon of stochastic resonance on diffusive, small-world and scale-free networks consisting of bistable overdamped oscillators. Important thereby is the fact that the external subthreshold periodic forcing is introduced only to a single oscillator of the network. Hence, the forcing acts as a pacemaker trying to impose its rhythm on the whole network through the unit to which it is introduced. Without the addition of additive spatiotemporal noise, however, the whole network, including the unit that is directly exposed to the pacemaker, remains trapped forever in one of the two stable steady states of the local dynamics. We show that the correlation between the frequency of subthreshold pacemaker activity and the response of the network is resonantly dependent on the intensity of additive noise. The reported pacemaker-driven stochastic resonance depends most significantly on the coupling strength and the underlying network structure. Namely, the outreach of the pacemaker obeys the classic diffusion law in the case of nearest-neighbor interactions, thus being proportional to the square root of the coupling strength, whereas it becomes superdiffusive by an appropriate small-world or scale-free topology of the interaction network. In particular, the scale-free topology is identified as being optimal for the dissemination of localized rhythmic activity across the whole network. Also, we show that the ratio between the clustering coefficient and the characteristic path length is the crucial quantity defining the ability of a small-world network to facilitate the outreach of the pacemaker-emitted subthreshold rhythm. We additionally confirm these findings by using the FitzHugh–Nagumo excitable system as an alternative to the bistable overdamped oscillator.