论文标题
具有对称性的神经网络模型的分叉
Bifurcations of a neural network model with symmetry
论文作者
论文摘要
我们分析了一个聚集的兴奋性抑制神经网络和由于网络中排列对称性而出现的基本分叉结构，因为全球耦合强度$ g $的变化是多种多样的。我们主要考虑两个网络拓扑：一个全面连接的网络，该网络不包括自我连接，以及一个将兴奋性细胞分解为相等大小的群集的网络。尽管在这两种情况下，分叉结构都由系统中的对称性确定，但两个系统的行为在质上不同。在全面连接的网络中，系统经历了HOPF分叉，导致定期轨道解决方案；值得注意的是，对于$ g $，有一个稳定的周期性轨道解决方案，没有稳定的固定点。相比之下，在集群网络中，没有Hopf分叉，并且有一个稳定的固定点，用于$ G $。
We analyze a family of clustered excitatory-inhibitory neural networks and the underlying bifurcation structures that arise because of permutation symmetries in the network as the global coupling strength $g$ is varied. We primarily consider two network topologies: an all-to-all connected network which excludes self-connections, and a network in which the excitatory cells are broken into clusters of equal size. Although in both cases the bifurcation structure is determined by symmetries in the system, the behavior of the two systems is qualitatively different. In the all-to-all connected network, the system undergoes Hopf bifurcations leading to periodic orbit solutions; notably, for large $g$, there is a single, stable periodic orbit solution and no stable fixed points. By contrast, in the clustered network, there are no Hopf bifurcations, and there is a family of stable fixed points for large $g$.
