School of Mathematics, South China University of Technology, Guangzhou, China.
Division of Computational Science and Technology, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden.
Elife. 2024 Mar 13;12:RP88777. doi: 10.7554/eLife.88777.
Oscillations arise in many real-world systems and are associated with both functional and dysfunctional states. Whether a network can oscillate can be estimated if we know the strength of interaction between nodes. But in real-world networks (in particular in biological networks) it is usually not possible to know the exact connection weights. Therefore, it is important to determine the structural properties of a network necessary to generate oscillations. Here, we provide a proof that uses dynamical system theory to prove that an odd number of inhibitory nodes and strong enough connections are necessary to generate oscillations in a single cycle threshold-linear network. We illustrate these analytical results in a biologically plausible network with either firing-rate based or spiking neurons. Our work provides structural properties necessary to generate oscillations in a network. We use this knowledge to reconcile recent experimental findings about oscillations in basal ganglia with classical findings.
在许多现实世界的系统中都会出现震荡现象，并且震荡与功能和非功能状态都有关联。如果我们知道节点之间的相互作用强度，就可以估计网络是否会发生震荡。但是在现实世界的网络中（特别是在生物网络中），通常不可能知道确切的连接权重。因此，确定生成震荡所需的网络结构特性非常重要。在这里，我们提供了一个使用动力系统理论的证明，证明了在单个循环阈值线性网络中，奇数个抑制节点和足够强的连接是产生震荡所必需的。我们在具有基于发放率或尖峰神经元的生物上合理的网络中说明了这些分析结果。我们的工作提供了在网络中产生震荡所需的结构特性。我们利用这些知识调和基底神经节震荡的最新实验发现与经典发现之间的矛盾。
