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Cascades on a stochastic pulse-coupled network

While much recent research has focused on understanding isolated cascades of networks, less attention has been given to dynamical processes on networks exhibiting repeated cascades of opposing influence. An example of this is the dynamic behaviour of financial markets where cascades of buying and se...

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Detalles Bibliográficos
Autores principales: Wray, C. M., Bishop, S. R.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2014
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4161966/
https://www.ncbi.nlm.nih.gov/pubmed/25213626
http://dx.doi.org/10.1038/srep06355
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author Wray, C. M.
Bishop, S. R.
author_facet Wray, C. M.
Bishop, S. R.
author_sort Wray, C. M.
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description While much recent research has focused on understanding isolated cascades of networks, less attention has been given to dynamical processes on networks exhibiting repeated cascades of opposing influence. An example of this is the dynamic behaviour of financial markets where cascades of buying and selling can occur, even over short timescales. To model these phenomena, a stochastic pulse-coupled oscillator network with upper and lower thresholds is described and analysed. Numerical confirmation of asynchronous and synchronous regimes of the system is presented, along with analytical identification of the fixed point state vector of the asynchronous mean field system. A lower bound for the finite system mean field critical value of network coupling probability is found that separates the asynchronous and synchronous regimes. For the low-dimensional mean field system, a closed-form equation is found for cascade size, in terms of the network coupling probability. Finally, a description of how this model can be applied to interacting agents in a financial market is provided.
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spelling pubmed-41619662014-09-22 Cascades on a stochastic pulse-coupled network Wray, C. M. Bishop, S. R. Sci Rep Article While much recent research has focused on understanding isolated cascades of networks, less attention has been given to dynamical processes on networks exhibiting repeated cascades of opposing influence. An example of this is the dynamic behaviour of financial markets where cascades of buying and selling can occur, even over short timescales. To model these phenomena, a stochastic pulse-coupled oscillator network with upper and lower thresholds is described and analysed. Numerical confirmation of asynchronous and synchronous regimes of the system is presented, along with analytical identification of the fixed point state vector of the asynchronous mean field system. A lower bound for the finite system mean field critical value of network coupling probability is found that separates the asynchronous and synchronous regimes. For the low-dimensional mean field system, a closed-form equation is found for cascade size, in terms of the network coupling probability. Finally, a description of how this model can be applied to interacting agents in a financial market is provided. Nature Publishing Group 2014-09-12 /pmc/articles/PMC4161966/ /pubmed/25213626 http://dx.doi.org/10.1038/srep06355 Text en Copyright © 2014, Macmillan Publishers Limited. All rights reserved http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder in order to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
spellingShingle Article
Wray, C. M.
Bishop, S. R.
Cascades on a stochastic pulse-coupled network
title Cascades on a stochastic pulse-coupled network
title_full Cascades on a stochastic pulse-coupled network
title_fullStr Cascades on a stochastic pulse-coupled network
title_full_unstemmed Cascades on a stochastic pulse-coupled network
title_short Cascades on a stochastic pulse-coupled network
title_sort cascades on a stochastic pulse-coupled network
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4161966/
https://www.ncbi.nlm.nih.gov/pubmed/25213626
http://dx.doi.org/10.1038/srep06355
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