Izhikevich E M
Center for Systems Science and Engineering, Arizona State University, Tempe, AZ 85287-7606, USA.
IEEE Trans Neural Netw. 1999;10(3):499-507. doi: 10.1109/72.761707.
Many scientists believe that all pulse-coupled neural networks are toy models that are far away from the biological reality. We show here, however, that a huge class of biophysically detailed and biologically plausible neural-network models can be transformed into a canonical pulse-coupled form by a piece-wise continuous, possibly noninvertible, change of variables. Such transformations exist when a network satisfies a number of conditions; e.g., it is weakly connected; the neurons are Class 1 excitable (i.e., they can generate action potentials with an arbitrary small frequency); and the synapses between neurons are conventional (i.e., axo-dendritic and axo-somatic). Thus, the difference between studying the pulse-coupled model and Hodgkin-Huxley-type neural networks is just a matter of a coordinate change. Therefore, any piece of information about the pulse-coupled model is valuable since it tells something about all weakly connected networks of Class 1 neurons. For example, we show that the pulse-coupled network of identical neurons does not synchronize in-phase. This confirms Ermentrout's result that weakly connected Class 1 neurons are difficult to synchronize, regardless of the equations that describe dynamics of each cell.
许多科学家认为，所有脉冲耦合神经网络都是远离生物现实的玩具模型。然而，我们在此表明，通过分段连续、可能不可逆的变量变换，一大类具有生物物理细节且符合生物学原理的神经网络模型可以转化为规范的脉冲耦合形式。当网络满足若干条件时，这种变换就会存在；例如，它是弱连接的；神经元是1类可兴奋的（即它们能够以任意小的频率产生动作电位）；并且神经元之间的突触是传统的（即轴突-树突型和轴突-胞体型）。因此，研究脉冲耦合模型与霍奇金-赫胥黎型神经网络之间的差异仅仅是坐标变换的问题。所以，关于脉冲耦合模型的任何一条信息都是有价值的，因为它能揭示有关所有1类神经元弱连接网络的一些情况。例如，我们表明相同神经元的脉冲耦合网络不会同相同步。这证实了厄门特劳特的结果，即弱连接的1类神经元难以同步，无论描述每个细胞动态的方程是什么。
