scholarly journals Spatial coherence resonance on diffusive and small-world networks of Hodgkin–Huxley neurons

2008 ◽  
Vol 18 (2) ◽  
pp. 023102 ◽  
Author(s):  
Xiaojuan Sun ◽  
Matjaž Perc ◽  
Qishao Lu ◽  
Jürgen Kurths
Keyword(s):  
Spatial Coherence ◽  
Small World ◽  
Small World Networks ◽  
Coherence Resonance

SPATIAL COHERENCE RESONANCE IN DELAYED HODGKIN–HUXLEY NEURONAL NETWORKS

2010 ◽  
Vol 24 (09) ◽  
pp. 1201-1213 ◽  
Author(s):  
QING YUN WANG ◽  
MATJAŽ PERC ◽  
ZHI SHENG DUAN ◽  
GUAN RONG CHEN
Keyword(s):  
Information Transmission ◽  
Noise Level ◽  
Neuronal Networks ◽  
Spatial Coherence ◽  
Spatial Dynamics ◽  
Small World ◽  
Transmission Delay ◽  
Small World Networks ◽  
Coherence Resonance ◽  
Short Delay

We study the phenomenon of spatial coherence resonance (SCR) on Hodgkin–Huxley (HH) neuronal networks that are characterized with information transmission delay. In particular, we examine the ability of additive Gaussian noise to optimally extract a particular spatial frequency of excitatory waves in diffusive and small-world networks on which information transmission amongst directly connected neurons is not instantaneous. On diffusively coupled HH networks, we find that for short delay lengths, there always exists an intermediate noise level by which the noise-induced spatial dynamics is maximally ordered, hence implying the possibility of SCR in the system. Importantly thereby, the noise level warranting optimally ordered excitatory waves increases linearly with the increasing delay time, suggesting that extremely long delays might nevertheless preclude the observation of SCR on diffusive networks. Moreover, we find that the small-world topology introduces another obstacle for the emergence of ordered spatial dynamics out of noise because the magnitude of SCR fades progressively as the fraction of rewired links increases, hence evidencing decoherence of noise-induced spatial dynamics on delayed small-world HH networks. Presented results thus provide insights that could facilitate the understanding of the joint impact of noise and information transmission delay on realistic neuronal networks.

Networks

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Complex Systems ◽  
Complex Networks ◽  
Phase Diagrams ◽  
Community Detection ◽  
Network Science ◽  
Small World ◽  
Small World Networks ◽  
Multilayer Networks ◽  
Basic Vocabulary

Understanding the interactions between the components of a system is key to understanding it. In complex systems, interactions are usually not uniform, not isotropic and not homogeneous: each interaction can be specific between elements.Networks are a tool for keeping track of who is interacting with whom, at what strength, when, and in what way. Networks are essential for understanding of the co-evolution and phase diagrams of complex systems. Here we provide a self-contained introduction to the field of network science. We introduce ways of representing and handle networks mathematically and introduce the basic vocabulary and definitions. The notions of random- and complex networks are reviewed as well as the notions of small world networks, simple preferentially grown networks, community detection, and generalized multilayer networks.

scholarly journals Multifractal analysis of eigenvectors of small-world networks

2021 ◽  
Vol 144 ◽  
pp. 110745
Author(s):  
Ankit Mishra ◽  
Jayendra N. Bandyopadhyay ◽  
Sarika Jalan
Keyword(s):  
Multifractal Analysis ◽  
Small World ◽  
Small World Networks
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