标题： Theta模型中环形突触连接神经元的旋转波 显示英文标题

标题： Rotating waves in the Theta model for a ring of synaptically connected neurons

摘要： 我们研究了Theta模型中环形耦合神经元的旋转波。我们证明，当神经元是振荡型时，至少存在一个旋转波。对于可激发型神经元，在弱突触耦合情况下，我们证明不存在行波；而在强突触耦合情况下，至少存在两个旋转波，一个“快速”旋转波和一个“慢速”旋转波。我们推导出“临界”耦合强度以及波速的显式上下界。我们还研究了均匀耦合的特殊情况，在这种情况下可以得到关于旋转波的完整解析结果。 显示英文摘要

摘要： We study rotating waves in the Theta model for a ring of synaptically-interacting neurons. We prove that when the neurons are oscillatory, at least one rotating wave always exists. In the case of excitable neurons, we prove that no travelling waves exist when the synaptic coupling is weak, and at least two rotating waves, a `fast' one and a `slow' one, exist when the synaptic coupling is sufficiently strong. We derive explicit upper and lower bounds for the `critical' coupling strength as well as for wave velocities. We also study the special case of uniform coupling, in which complete analytical results on the rotating waves can be achieved.