Erdens-Rényi网络、规则随机网络、环格和全对全神经网络中的独特动力学行为
Distinct dynamical behavior in Erdős-Rényi networks, regular random networks, ring lattices, and all-to-all neuronal networks
摘要：
神经元网络动力学依赖于网络结构。在本文中，我们研究了网络拓扑结构如何支持神经网络中不同动力学行为的出现。特别是，我们考虑神经网络动力学的Erdens-Rényi（ER）网络，规则随机（RR）网络，环格，和所有的网络。我们解析地解决了随机二进制状态神经元在所有的网络拓扑结构，除了环格的神经网络模型。鉴于除了网络结构之外，所有四种模型都是等价的，这使我们能够理解网络结构在神经网络动力学中的作用。虽然ER和RR网络具有相似的相图，但我们在全对全网络中发现了惊人不同的相图。神经元网络动力学不仅在某些参数范围内是不同的，而且它也经历了不同的分叉（与全对全网络相比，ER和RR中的分叉库更丰富）。这表明，局部异质性之间的比率兴奋和抑制起着至关重要的作用，涌现动力学。此外，我们还观察到ER和RR网络之间的一个细微差异，即ER网络在较低的噪声水平下比RR网络经历神经元活动跳跃，这可能是由于ER网络的程度异质性在RR网络中不存在。最后，RR网络和环格网络振荡之间的比较表明，小世界性质在维持稳定的网络振荡的重要性。
英文摘要：
Neuronal network dynamics depends on network structure. In this paper we study how network topology underpins the emergence of different dynamical behaviors in neuronal networks. In particular, we consider neuronal network dynamics on Erdős-Rényi (ER) networks, regular random (RR) networks, ring lattices, and all-to-all networks. We solve analytically a neuronal network model with stochastic binary-state neurons in all the network topologies, except ring lattices. Given that apart from network structure, all four models are equivalent, this allows us to understand the role of network structure in neuronal network dynamics. Whilst ER and RR networks are characterized by similar phase diagrams, we find strikingly different phase diagrams in the all-to-all network. Neuronal network dynamics is not only different within certain parameter ranges, but it also undergoes different bifurcations (with a richer repertoire of bifurcations in ER and RR compared to all-to-all networks). This suggests that local heterogeneity in the ratio between excitation and inhibition plays a crucial role on emergent dynamics. Furthermore, we also observe one subtle discrepancy between ER and RR networks, namely ER networks undergo a neuronal activity jump at lower noise levels compared to RR networks, presumably due to the degree heterogeneity in ER networks that is absent in RR networks. Finally, a comparison between network oscillations in RR networks and ring lattices shows the importance of small-world properties in sustaining stable network oscillations.
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