Zhu Jinjie, Liu Xianbin
State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
Chaos. 2017 Aug;27(8):083114. doi: 10.1063/1.4998927.
In this paper, the collective behaviors for ring structured bursting neuronal networks with electrical couplings and distance-dependent delays are studied. Each neuron is modeled by the Hindmarsh-Rose neuron. Through changing time delays between connected neurons, different spatiotemporal patterns are obtained. These patterns can be explained by calculating the ratios between the bursting period and the delay which exhibit clear locking relations. The holding and the failure of the lockings are investigated via bifurcation analysis. In particular, the bursting death phenomenon is observed for large coupling strengths and small time delays which is in fact the result of the partial amplitude death in the fast subsystem. These results indicate that the collective behaviors of bursting neurons critically depend on the bifurcation structure of individual ones and thus the variety of bifurcation types for bursting neurons may create diverse behaviors in similar neuronal ensembles.
本文研究了具有电耦合和距离依赖延迟的环形结构爆发式神经网络的集体行为。每个神经元由Hindmarsh-Rose神经元建模。通过改变连接神经元之间的时间延迟，获得了不同的时空模式。这些模式可以通过计算爆发周期与延迟之间的比率来解释，该比率呈现出明显的锁定关系。通过分岔分析研究了锁定的保持和失效。特别地，在大耦合强度和小时间延迟下观察到爆发死亡现象，这实际上是快速子系统中部分振幅死亡的结果。这些结果表明，爆发神经元的集体行为关键取决于单个神经元的分岔结构，因此爆发神经元分岔类型的多样性可能在相似的神经元集合中产生不同的行为。
