耦合演化神经元网络中的自组织临界性研究

Self-Organized Criticality of the Co-Evolutionary Neuronal Network

摘要: 本文借助类Bak-Sneppen (BS)神经元，对稳定的耦合演化网络结构进行了自组织临界性研究。网络中的节点为类BS神经元，节点之间的连边表示神经元之间的突触。在演化过程中，将均匀分布的障碍值统一随机分配给神经元，选择具备最小障碍值即最不稳定的神经元进行“放电”，从而改变自己和最近邻神经元的障碍值，放电神经元随后将处于不应期。本研究主要模拟了耦合神经元网络结构在稳定条件下的雪崩规模分布，首回归时间分布和全回归时间分布，发现其均具有幂律分布特性。另外，在雪崩参数取值在0.45附近时，雪崩规模分布的幂律系数为−1.5，与已有实验结果相吻合。研究结果表明，当耦合演化网络具有稳定结构时，类BS神经元表现出自组织临界性。

Abstract: This study investigates the self-organized criticality (SOC) of stable coupled evolutionary neuronal network by employing Bak-Sneppen (BS)-like neurons. In the network, nodes represent BS-like neurons, while edges denote synapses between neurons. During the evolutionary process, barrier values uniformly distributed in the range are randomly assigned to neurons. The neuron with the smallest barrier value, i.e., the most unstable one, is selected to “fire”, thereby altering its own barrier value as well as those of its nearest neighbors. The firing neuron subsequently enters a refractory period. This research primarily simulates the avalanche size distribution, first return time distribution, and all return time distribution under stable conditions in coupled evolutionary neuronal network, revealing their power-law characteristics. Notably, when the avalanche parameter is approximately 0.45, the power-law exponent of the avalanche size distribution is −1.5, consistent with experimental results. These findings indicate that BS-like neurons exhibit self-organized criticality when co-evolutionary neuronal network possess stable structures.