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Graph-facilitated resonant mode counting in stochastic interaction networks

Adamer, Michael, Woolley, Thomas ORCID: 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

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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
Date of First Compliant Deposit: 19 December 2017
Date of Acceptance: 24 November 2017
Last Modified: 16 Nov 2023 12:26

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