Laing Carlo R, Bläsche Christian, Means Shawn
School of Natural and Computational Sciences, Massey University, Auckland, New Zealand.
Front Syst Neurosci. 2021 Feb 10;15:631377. doi: 10.3389/fnsys.2021.631377. eCollection 2021.
Winfree oscillators are phase oscillator models of neurons, characterized by their phase response curve and pulsatile interaction function. We use the Ott/Antonsen ansatz to study large heterogeneous networks of Winfree oscillators, deriving low-dimensional differential equations which describe the evolution of the expected state of networks of oscillators. We consider the effects of correlations between an oscillator's in-degree and out-degree, and between the in- and out-degrees of an "upstream" and a "downstream" oscillator (degree assortativity). We also consider correlated heterogeneity, where some property of an oscillator is correlated with a structural property such as degree. We finally consider networks with parameter assortativity, coupling oscillators according to their intrinsic frequencies. The results show how different types of network structure influence its overall dynamics.
温弗里振荡器是神经元的相位振荡器模型，其特征在于它们的相位响应曲线和脉冲相互作用函数。我们使用奥尔特/安东森假设来研究温弗里振荡器的大型异构网络，推导低维微分方程，这些方程描述了振荡器网络预期状态的演变。我们考虑振荡器的入度和出度之间、以及“上游”和“下游”振荡器的入度与出度之间的相关性影响（度相关性）。我们还考虑相关异质性，即振荡器的某些属性与诸如度等结构属性相关。我们最后考虑具有参数相关性的网络，根据振荡器的固有频率耦合振荡器。结果展示了不同类型的网络结构如何影响其整体动力学。
