Pulse Bifurcations in Stochastic Neural Fields
Pulse Bifurcations in Stochastic Neural Fields
复制标题
随机神经场中的脉冲分岔
DOI：
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发表时间：
2014
影响因子：
2.1
通讯作者：
Grégory Faye
中科院分区：
文献类型：
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作者：
Z. Kilpatrick;Grégory Faye
研究了线性自适应空间扩展神经场中加性噪声对行脉冲解的影响。神经场是带有一个积分项的演化方程，它描述了网络不同空间位置的神经元之间的突触相互作用。我们引入一个辅助变量来模拟局部负反馈的影响，并通过将系统建模为一组空间扩展的朗之万方程来考虑随机涨落，该方程的噪声项为$Q$-Wiener过程。由于网络的平移不变性，神经场可以支持空间局域凸起解的连续体，这些解可以通过增加自适应的强度来破坏稳定，从而产生行波脉冲解。在这一临界点附近，我们导出了一个描述当噪声和确定性不稳定性具有相似量级时这些分叉脉冲的动力学的随机振幅方程。离开这一分叉，我们研究了添加剂的影响。
We study the effects of additive noise on traveling pulse solutions in spatially extended neural fields with linear adaptation. Neural fields are evolution equations with an integral term characterizing synaptic interactions between neurons at different spatial locations of the network. We introduce an auxiliary variable to model the effects of local negative feedback and consider random fluctuations by modeling the system as a set of spatially extended Langevin equations whose noise term is a $Q$-Wiener process. Due to the translation invariance of the network, neural fields can support a continuum of spatially localized bump solutions that can be destabilized by increasing the strength of the adaptation, giving rise to traveling pulse solutions. Near this criticality, we derive a stochastic amplitude equation describing the dynamics of these bifurcating pulses when the noise and the deterministic instability are of comparable magnitude. Away from this bifurcation, we investigate the effects of additive ...
DOI：
10.1098/rstb.2000.0769
发表时间：
2001-03-29
影响因子：
6.3
作者：
Bressloff, PC;Cowan, JD;Wiener, MC
通讯作者：
Wiener, MC
影响因子：
33.6
作者：
Wang XJ
通讯作者：
Wang XJ
影响因子：
1.7
作者：
Bloemker, D.;Hairer, M.;Pavliotis, G. A.
通讯作者：
Pavliotis, G. A.