Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics
Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics
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DOI：
10.1103/physreve.82.051903
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发表时间：
2010-11-03
影响因子：
2.4
通讯作者：
Bressloff, Paul C.
中科院分区：
文献类型：
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作者：
Bressloff, Paul C.
我们分析了一个带有本征噪声的神经元种群动力学随机模型。在热力学极限N中，N决定了每个种群的大小，动力学由确定性的威尔逊-考恩方程描述。另一方面，对于有限的N，动态由确定每个种群内的尖峰活动的概率的主方程来描述。我们首先考虑在确定性极限下呈现双稳的单个激发布居。随机网络的稳态概率分布在确定性网络的稳定不动点对应的点处有极大值，这两个极大值的相对权重取决于系统的大小。对于大但有限的N，我们使用Wentzel-Kramers-Brillouin(WKB)近似和匹配的渐近展开，计算了由噪声引起的亚稳态之间的指数小跃迁速率。然后，我们考虑一个支持极限环振荡的两种群兴奋或抑制网络。利用扩散近似，我们将动力学简化为一个神经朗之万方程，并展示了本征噪声如何放大亚阈值振荡(准周期)。
We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit N ->infinity, where N determines the size of each population, the dynamics is described by deterministic Wilson-Cowan equations. On the other hand, for finite N the dynamics is described by a master equation that determines the probability of spiking activity within each population. We first consider a single excitatory population that exhibits bistability in the deterministic limit. The steady-state probability distribution of the stochastic network has maxima at points corresponding to the stable fixed points of the deterministic network; the relative weighting of the two maxima depends on the system size. For large but finite N, we calculate the exponentially small rate of noise-induced transitions between the resulting metastable states using a Wentzel-Kramers-Brillouin (WKB) approximation and matched asymptotic expansions. We then consider a two-population excitatory or inhibitory network that supports limit cycle oscillations. Using a diffusion approximation, we reduce the dynamics to a neural Langevin equation, and show how the intrinsic noise amplifies subthreshold oscillations (quasicycles).