Oscillation sources and wave propagation paths in complex networks consisting of excitable nodes

Liao, Xuhong; Qian, Yu; Mi, Yuanyuan; Xia, Qinzhi; Huang, Xiaoqing; Hu, Gang

doi:10.1007/s11467-010-0152-1

Cited by 22 publications

(17 citation statements)

References 28 publications

(32 reference statements)

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“…How network topology can facilitate the selfsustainment of excitable dynamics on graphs is a fundamental question about the organization of dynamics on graphs [7,8,16,35]. The role of cycles in excitable dynamics on graphs has received a remarkable amount of attention in the last years [22,25,34], in particular in Computational Neuroscience [19,38]. Cycles have been implicated in maintaining activity in a network [25,38].…”

Section: Introductionmentioning

confidence: 99%

Topological determinants of self-sustained activity in a simple model of excitable dynamics on graphs

Fretter

Lesne

Hilgetag

et al. 2017

Sci Rep

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Simple models of excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This topic is of practical relevance to diverse fields, ranging from neuroscience to engineering. Here we analyze how a single excitation propagates through a random network as a function of the excitation threshold, that is, the relative amount of activity in the neighborhood required for the excitation of a node. We observe that two sharp transitions delineate a region of sustained activity. Using analytical considerations and numerical simulation, we show that these transitions originate from the presence of barriers to propagation and the excitation of topological cycles, respectively, and can be predicted from the network topology. Our findings are interpreted in the context of network reverberations and self-sustained activity in neural systems, which is a question of long-standing interest in computational neuroscience.

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Section: Introductionmentioning

confidence: 99%

Topological determinants of self-sustained activity in a simple model of excitable dynamics on graphs

Fretter

Lesne

Hilgetag

et al. 2017

Sci Rep

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“…Roxin et al ( 2004 ) has shown, for integrate-and-fire neurons, that a very low density of shortcuts was sufficient to generate persistent activity from a local stimulus through the re-injection of activity into previously excited domains. In a continuous setting Qian et al ( 2010b ) and Liao et al ( 2011 ) demonstrated the existence of phase-advanced driving links, revealing possible self-organized structures supporting self-sustained oscillations. Another study (Qian et al, 2010a ) analyzed diverse self-sustained oscillatory patterns and their mechanisms in small-world networks of excitable nodes, showing that spatiotemporal patterns are sensitive to long-range connection probability and coupling intensity.…”

Section: Introductionmentioning

confidence: 99%

Building Blocks of Self-Sustained Activity in a Simple Deterministic Model of Excitable Neural Networks

García¹,

Lesne²,

Hütt³

et al. 2012

Front. Comput. Neurosci.

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Understanding the interplay of topology and dynamics of excitable neural networks is one of the major challenges in computational neuroscience. Here we employ a simple deterministic excitable model to explore how network-wide activation patterns are shaped by network architecture. Our observables are co-activation patterns, together with the average activity of the network and the periodicities in the excitation density. Our main results are: (1) the dependence of the correlation between the adjacency matrix and the instantaneous (zero time delay) co-activation matrix on global network features (clustering, modularity, scale-free degree distribution), (2) a correlation between the average activity and the amount of small cycles in the graph, and (3) a microscopic understanding of the contributions by 3-node and 4-node cycles to sustained activity.

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“…Our statements about self-organized patterns on graphs have been exemplified for the case of excitable dynamics. As illustrated by a range of investigations, wave phenomena ( 34 , 36 , 54 ), as well as spiral waves and other self-organized dynamical phenomena of excitations on graphs ( 43 , 54 – 56 ), are contributing to the systematic relationship between network topology and dynamics ( 5 , 57 ). Our investigation addresses the emergence of link-usage asymmetry in excitable dynamics on networks and, in particular, how self-organized collective excitation patterns contribute to this asymmetry.…”

Section: Discussionmentioning

confidence: 99%

Link-usage asymmetry and collective patterns emerging from rich-club organization of complex networks

Moretti

Hütt

2020

Proc. Natl. Acad. Sci. U.S.A.

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In models of excitable dynamics on graphs, excitations can travel in both directions of an undirected link. However, as a striking interplay of dynamics and network topology, excitations often establish a directional preference. Some of these cases of “link-usage asymmetry” are local in nature and can be mechanistically understood, for instance, from the degree gradient of a link (i.e., the difference in node degrees at both ends of the link). Other contributions to the link-usage asymmetry are instead, as we show, self-organized in nature, and strictly nonlocal. This is the case for excitation waves, where the preferential propagation of excitations along a link depends on its orientation with respect to a hub acting as a source, even if the link in question is several steps away from the hub itself. Here, we identify and quantify the contribution of such self-organized patterns to link-usage asymmetry and show that they extend to ranges significantly longer than those ascribed to local patterns. We introduce a topological characterization, the hub-set-orientation prevalence of a link, which indicates its average orientation with respect to the hubs of a graph. Our numerical results show that the hub-set-orientation prevalence of a link strongly correlates with the preferential usage of the link in the direction of propagation away from the hub core of the graph. Our methodology is embedding-agnostic and allows for the measurement of wave signals and the sizes of the cores from which they originate.

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Oscillation sources and wave propagation paths in complex networks consisting of excitable nodes

Cited by 22 publications

References 28 publications

Topological determinants of self-sustained activity in a simple model of excitable dynamics on graphs

Topological determinants of self-sustained activity in a simple model of excitable dynamics on graphs

Building Blocks of Self-Sustained Activity in a Simple Deterministic Model of Excitable Neural Networks

Link-usage asymmetry and collective patterns emerging from rich-club organization of complex networks

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