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- Title
Cascades on a stochastic pulse-coupled network.
- Authors
Wray, C. M.; Bishop, S. R.
- Abstract
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. Alower 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.
- Subjects
FINANCIAL markets; ELECTRIC oscillators; MEAN field theory; STATISTICAL mechanics; COUPLING reactions (Chemistry); CHEMICAL reactions
- Publication
Scientific Reports, 2014, p1
- ISSN
2045-2322
- Publication type
Article
- DOI
10.1038/srep06355