Cardiff University | Prifysgol Caerdydd ORCA
Online Research @ Cardiff 
WelshClear Cookie - decide language by browser settings

Graph-facilitated resonant mode counting in stochastic interaction networks

Adamer, Michael, Woolley, Thomas and Harrington, Heather 2017. Graph-facilitated resonant mode counting in stochastic interaction networks. Journal of the Royal Society Interface 14 (137) , 20170447. 10.1098/rsif.2017.0447

[img]
Preview
PDF - Accepted Post-Print Version
Download (700kB) | Preview

Abstract

Oscillations in dynamical systems are widely reported in multiple branches of applied mathematics. Critically, even a non-oscillatory deterministic system can produce cyclic trajectories when it is in a low copy number, stochastic, regime. Common methods of finding parameter ranges for stochastically-driven resonances, such as direct calculation, are cumbersome for any but the smallest networks. In this paper we provide a systematic framework to efficiently determine the number of resonant modes and parameter ranges for stochastic oscillations relying on real root counting algorithms and graph theoretic methods. We argue that stochastic resonance is a network property by showing that resonant modes only depend on the squared Jacobian matrix $J^2$, unlike deterministic oscillations which are determined by $J$. By using graph theoretic tools, analysis of stochastic behaviour for larger interaction networks is simplified and stochastic dynamical systems with multiple resonant modes can be identified easily.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: The Royal Society
ISSN: 1742-5689
Last Modified: 20 Dec 2017 05:28
URI: http://orca.cf.ac.uk/id/eprint/107585

Citation Data

Cited 1 time in Google Scholar. View in Google Scholar

Cited 1 time in Scopus. View in Scopus. Powered By Scopus® Data

Actions (repository staff only)

Edit Item Edit Item

Downloads

Downloads per month over past year

View more statistics