Lytton William W, Hines Michael L
Department of Physiology, Pharmacology, and Neurology, State University of New York, Downstate, Brooklyn, NY 11203-2098, USA.
Neural Comput. 2005 Apr;17(4):903-21. doi: 10.1162/0899766053429453.
Realistic neural networks involve the coexistence of stiff, coupled, continuous differential equations arising from the integrations of individual neurons, with the discrete events with delays used for modeling synaptic connections. We present here an integration method, the local variable time-step method (lvardt), that uses separate variable-step integrators for individual neurons in the network. Cells that are undergoing excitation tend to have small time steps, and cells that are at rest with little synaptic input tend to have large time steps. A synaptic input to a cell causes reinitialization of only that cell's integrator without affecting the integration of other cells. We illustrated the use of lvardt on three models: a worst-case synchronizing mutual-inhibition model, a best-case synfire chain model, and a more realistic thalamocortical network model.
现实的神经网络涉及由单个神经元整合产生的刚性、耦合、连续微分方程与用于对突触连接进行建模的具有延迟的离散事件的共存。我们在此提出一种积分方法，即局部可变时间步长方法（lvardt），该方法对网络中的单个神经元使用单独的可变步长积分器。正在经历兴奋的细胞往往具有较小的时间步长，而处于静止状态且几乎没有突触输入的细胞往往具有较大的时间步长。对一个细胞的突触输入只会导致该细胞积分器的重新初始化，而不会影响其他细胞的积分。我们展示了lvardt在三个模型上的应用：一个最坏情况的同步相互抑制模型、一个最佳情况的同步发放链模型以及一个更现实的丘脑皮质网络模型。
