Denman-Johnson M, Coombes S
Department of Mathematical Sciences, Loughborough University, Leicestershire, LE11 3TU, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 May;67(5 Pt 1):051903. doi: 10.1103/PhysRevE.67.051903. Epub 2003 May 6.
The McKean model of a neuron possesses a one-dimensional fast voltagelike variable and a slow recovery variable. A recent geometric analysis of the singularly perturbed system has allowed an explicit construction of its phase response curve [S. Coombes, Physica D 160, 173 (2001)]. Here we use tools from coupled oscillator theory to study weakly coupled networks of McKean neurons. Using numerical techniques, we show that the McKean system has traveling wave phase-locked solutions consistent with that of a network of more biophysically detailed Hodgkin-Huxley neurons.
神经元的麦基恩模型具有一个一维的类似电压的快速变量和一个缓慢的恢复变量。最近对该奇异摄动系统的几何分析使得能够明确构建其相位响应曲线[S. 库姆斯，《物理D》160, 173 (2001)]。在这里，我们使用耦合振子理论的工具来研究麦基恩神经元的弱耦合网络。通过数值技术，我们表明麦基恩系统具有与生物物理细节更丰富的霍奇金 - 赫胥黎神经元网络一致的行波锁相解。
