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| | 活动凸起的一个可能的计算角色是根据空间结构化网络中凸起的峰值位置对一组刺激特征进行编码。在同构网络的情况下，允许的特征集将形成反映网络底层拓扑的连续流形（吸引子）。因此，周期性刺激特征可以由同质环网络中的活动凸起编码（Ben-Yishai 等人 1995，Zhang 1995）。然而，同质网络的后果之一是，相对于与连续流形相切的空间平移，凹凸将略微稳定。这意味着在存在任意小的噪声水平的情况下，活动颠簸会随着时间缓慢漂移（Laing 和 Chow 2001）。构建对噪声具有鲁棒性的神经场模型的一种方法是引入某种形式的细胞双稳态（Camperi and Wang 1998，Fall et al 2004）。 | | 活动凸起的一个可能的计算角色是根据空间结构化网络中凸起的峰值位置对一组刺激特征进行编码。在同构网络的情况下，允许的特征集将形成反映网络底层拓扑的连续流形（吸引子）。因此，周期性刺激特征可以由同质环网络中的活动凸起编码（Ben-Yishai 等人 1995，Zhang 1995）。然而，同质网络的后果之一是，相对于与连续流形相切的空间平移，凹凸将略微稳定。这意味着在存在任意小的噪声水平的情况下，活动颠簸会随着时间缓慢漂移（Laing 和 Chow 2001）。构建对噪声具有鲁棒性的神经场模型的一种方法是引入某种形式的细胞双稳态（Camperi and Wang 1998，Fall et al 2004）。 |
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| − | ===Travelling Waves=== | + | ===行波=== |
| | [[Image:front_pulse_contract.jpg|thumb|right|200px|A travelling pulse in a one dimensional neural field model with [[spike frequency adaptation]].]] | | [[Image:front_pulse_contract.jpg|thumb|right|200px|A travelling pulse in a one dimensional neural field model with [[spike frequency adaptation]].]] |
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| − | For one-dimensional models with sigmoidal firing rate functions and excitatory coupling it is possible to find wave fronts joining an excited state to a resting state (Ermentrout & McLeod 1993). Moreover, in systems with mixed (excitatory and inhibitory) coupling or excitatory systems with adaptive currents, solitary travelling pulses are also possible.
| + | 对于具有 sigmoid 发射率函数和兴奋耦合的一维模型，可以找到将激发态连接到静止态的波前 (Ermentrout & McLeod 1993)。 此外，在具有混合（兴奋性和抑制性）耦合的系统或具有自适应电流的兴奋性系统中，单独的行进脉冲也是可能的。 对于具有阈值 h 的 Heaviside 发射率函数，已经获得了许多关于行波的精确结果。 例如，在 w(x)=exp(-|x|)/2 的纯兴奋性网络中，稳定行进前沿的速度采用显式形式 |
| − | For a Heaviside firing rate function with threshold h many exact results about travelling waves have been obtained. For example the speed of a stable travelling front in a purely excitatory network with w(x)=exp(-|x|)/2 takes the explicit form
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| − | The strong dependence of the wave speed on the threshold h has now been indirectly established in real neural tissue (rat cortical slices bathed in the [[GABA_A]] blocker [[picrotoxin]]) by Richardson <i>et al</i>. 2005. These experiments exploit the fact that cortical neurons have long apical [[dendrites]] and are easily polarisable by an electric field and that [[epileptiform]] bursts can be initiated by a stimulation electrode. An applied positive (negative) electric field across the slice increased (decreased) the speed of wave propagation, consistent with the theoretical predictions of neural field theory assuming that a positive (negative) electric field reduces (increases) the threshold h.
| + | 现在，Richardson 等人在真实的神经组织（浸泡在 GABA_A 阻滞剂印防己毒素中的大鼠皮质切片）中间接确定了波速对阈值 h 的强烈依赖性。 2005. 这些实验利用了这样一个事实，即皮质神经元具有长的顶端树突，并且很容易被电场极化，并且癫痫样爆发可以由刺激电极引发。跨切片施加的正（负）电场增加（降低）波传播速度，这与假设正（负）电场降低（增加）阈值 h 的神经场理论的理论预测一致。 |
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| | + | 行波的分岔结构可以使用所谓的埃文斯函数来分析。这最初是由 Evans (1975) 在关于霍奇金-赫胥黎类型的可兴奋神经轴突方程的稳定性定理的背景下制定的。这个复解析函数的零点决定了算子的法线谱，该算子是通过将系统关于其行波解进行线性化而获得的。神经场模型的扩展是最近才出现的，对于 Heaviside 放电率函数的特殊情况，现在已经研究了几个模型（Coombes & Owen 2004, 2005）。 |
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| − | The bifurcation structure of travelling waves can be analysed using a so-called [[Evans function]]. This was originally formulated
| + | 大多数神经场模型中的一个常见假设是网络是同质的和各向同性的，也就是说，权重分布取决于网络内交互种群之间的距离。然而，由于在皮层表层中发现的长程水平连接的斑块性质，真正的皮层更现实地被建模为各向异性和不均匀的二维介质（Bosking et al 1997）。重量分布的各向异性可能导致不同方向的波速变化，而不均匀性可能导致随时间变化的波剖面，并可能导致波传播失败（Bressloff 2001）。 |
| − | by Evans (1975) in the context of a stability theorem about
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| − | excitable nerve axon equations of [[Hodgkin-Huxley_Model|Hodgkin–Huxley]] type. The zeros of this complex analytic function determine the normal spectrum of the operator obtained by linearising a system about its travelling wave solution.
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| − | The extension to neural field models is more recent and, for the special case of a Heaviside firing rate function, several models have now been studied (Coombes & Owen 2004, 2005).
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| − | One of the common assumptions in most neural field models is that the network is homogeneous and isotropic, that is, the weight distribution depends on the distance between interacting populations within the network. The real cortex, however, is more realistically modeled as an anisotropic and inhomogeneous two-dimensional medium due to the patchy nature of long-range horizontal connections found in superficial layers of cortex (Bosking et al 1997). Anisotropies in the weight distribution could lead to variations in wave speed in different directions, whereas inhomogeneities could lead to time-varying wave profiles and possibly wave propagation failure (Bressloff 2001).
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