Comprehending how the brain functions requires an understanding of the dynamics of neuronal assemblies. Previous work used a mean-field reduction method to determine the collective dynamics of a large heterogeneous network of uniformly and globally coupled theta neurons, which are a canonical formulation of Type I neurons. However, in modeling neuronal networks, it is unreasonable to assume that the coupling strength between every pair of neurons is identical. The goal in the present work is to analytically examine the collective macroscopic behavior of a network of theta neurons that is more realistic in that it includes heterogeneity in the coupling strength as well as in neuronal excitability. We consider the occurrence of dynamical structures that give rise to complicated dynamics via bifurcations of macroscopic collective quantities, concentrating on two biophysically relevant cases: (1) predominantly excitable neurons with mostly excitatory connections, and (2) predominantly spiking neurons with inhibitory connections. We find that increasing the synaptic diversity moves these dynamical structures to distant extremes of parameter space, leaving simple collective equilibrium states in the physiologically relevant region. We also study the node vs. focus nature of stable macroscopic equilibrium solutions and discuss our results in the context of recent literature.

中文翻译：

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突触多样性抑制 Theta 神经元网络中的复杂集体行为

理解大脑如何运作需要了解神经元组件的动力学。以前的工作使用平均场减少方法来确定均匀和全局耦合的θ神经元的大型异构网络的集体动力学，这是 I 型神经元的典型公式。然而，在对神经元网络建模时，假设每对神经元之间的耦合强度相同是不合理的。目前工作的目标是分析检查 theta 神经元网络的集体宏观行为，该网络更现实，因为它包括耦合强度和神经元兴奋性的异质性。我们考虑通过宏观集体量的分叉产生复杂动力学的动力学结构的发生，专注于两个生物物理学相关的案例：（1）主要是兴奋性神经元，主要是兴奋性连接，（2）主要是具有抑制性连接的尖峰神经元。我们发现增加突触多样性将这些动态结构移动到参数空间的遥远极端，在生理相关区域留下简单的集体平衡状态。我们还研究了稳定宏观平衡解的节点与焦点性质，并在最近文献的背景下讨论了我们的结果。在生理相关区域留下简单的集体平衡状态。我们还研究了稳定宏观平衡解的节点与焦点性质，并在最近文献的背景下讨论了我们的结果。在生理相关区域留下简单的集体平衡状态。我们还研究了稳定宏观平衡解的节点与焦点性质，并在最近文献的背景下讨论了我们的结果。