Ermentrout Bard, Ko Tae-Wook
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
Philos Trans A Math Phys Eng Sci. 2009 Mar 28;367(1891):1097-115. doi: 10.1098/rsta.2008.0259.
We use weakly coupled oscillator theory to study the effects of delays on coupled systems of neuronal oscillators. We explore, first, simple pairs with constant delays and then examine the role of distributed delays as would occur in systems with dendritic branches or in networks where there is a distance-dependent conductance delay. In the latter, we use mean field theory to show the emergence of travelling waves and the loss of synchronization. Next, we consider phase models with stronger coupling and delays in the state variables. We show that they have a richer dynamics but one that is still similar to the weakly coupled case.
我们使用弱耦合振子理论来研究延迟对神经元振子耦合系统的影响。首先，我们探讨具有恒定延迟的简单对，然后研究分布式延迟的作用，这种延迟会出现在具有树突分支的系统中，或者出现在存在距离依赖性电导延迟的网络中。在后者中，我们使用平均场理论来展示行波的出现和同步的丧失。接下来，我们考虑状态变量中具有更强耦合和延迟的相位模型。我们表明它们具有更丰富的动力学，但仍然与弱耦合情况相似。
