Fotouhi M, Heidari M, Sharifitabar M
Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11365-9415, Tehran, Iran,
Biol Cybern. 2015 Jun;109(3):321-32. doi: 10.1007/s00422-015-0645-7. Epub 2015 Feb 13.
We introduce an extension of the classical neural field equation where the dynamics of the synaptic kernel satisfies the standard Hebbian type of learning (synaptic plasticity). Here, a continuous network in which changes in the weight kernel occurs in a specified time window is considered. A novelty of this model is that it admits synaptic weight decrease as well as the usual weight increase resulting from correlated activity. The resulting equation leads to a delay-type rate model for which the existence and stability of solutions such as the rest state, bumps, and traveling fronts are investigated. Some relations between the length of the time window and the bump width is derived. In addition, the effect of the delay parameter on the stability of solutions is shown. Also numerical simulations for solutions and their stability are presented.
我们引入了经典神经场方程的一种扩展形式，其中突触核的动力学满足标准的赫布型学习（突触可塑性）。在此，考虑一个连续网络，其中权重核的变化发生在特定的时间窗口内。该模型的一个新颖之处在于，它允许突触权重降低以及由相关活动导致的通常的权重增加。由此产生的方程导致了一个延迟型速率模型，我们研究了该模型中诸如静止状态、波峰和行波前沿等解的存在性和稳定性。推导了时间窗口长度与波峰宽度之间的一些关系。此外，还展示了延迟参数对解的稳定性的影响。同时给出了解及其稳定性的数值模拟结果。
