Fukai T, Tanaka S
Department of Electronics, Tokai University, Kanagawa, Japan.
Neural Comput. 1997 Jan 1;9(1):77-97. doi: 10.1162/neco.1997.9.1.77.
A neuroecological equation of the Lotka-Volterra type for mean firing rate is derived from the conventional membrane dynamics of a neural network with lateral inhibition and self-inhibition. Neural selection mechanisms employed by the competitive neural network receiving external inputs are studied with analytic and numerical calculations. A remarkable findings is that the strength of lateral inhibition relative to that of self-inhibition is crucial for determining the steady states of the network among three qualitatively different types of behavior. Equal strength of both types of inhibitory connections leads the network to the well-known winner-take-all behavior. If, however, the lateral inhibition is weaker than the self-inhibition, a certain number of neurons are activated in the steady states or the number of winners is in general more than one (the winners-share-all behavior). On the other hand, if the self-inhibition is weaker than the lateral one, only one neuron is activated, but the winner is not necessarily the neuron receiving the largest input. It is suggested that our simple network model provides a mathematical basis for understanding neural selection mechanisms.
一个基于具有侧向抑制和自我抑制的神经网络的传统膜动力学推导出来的、洛特卡 - 沃尔泰拉类型的平均放电率神经生态学方程。通过解析和数值计算研究了接收外部输入的竞争性神经网络所采用的神经选择机制。一个显著的发现是，相对于自我抑制而言，侧向抑制的强度对于在三种定性不同类型的行为中确定网络的稳态至关重要。两种类型的抑制性连接强度相等会使网络呈现出众所周知的胜者全得行为。然而，如果侧向抑制比自我抑制弱，在稳态下会有一定数量的神经元被激活，或者胜者的数量通常不止一个（胜者共享行为）。另一方面，如果自我抑制比侧向抑制弱，只有一个神经元被激活，但胜者不一定是接收最大输入的神经元。有人认为，我们的简单网络模型为理解神经选择机制提供了数学基础。
