2017/02/28 by Michael F. Adamer, Thomas E. Woolley, Adamer, Michael F +3
Biochemistry, Genetics and Molecular Biology · Computer Science · #Advanced Fluorescence Microscopy Techniques #Biological Physics (physics.bio-ph) #FOS: Biological sciences #FOS: Physical sciences #Gene Regulatory Network Analysis #Molecular Networks (q-bio.MN) #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.1702.08747
openalex publication_date 2017/02/28 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
Oscillations in a stochastic dynamical system, whose deterministic\ncounterpart has a stable steady state, are a widely reported phenomenon.\nTraditional methods of finding parameter regimes for stochastically-driven\nresonances are, however, cumbersome for any but the smallest networks. In this\nletter we show by example of the Brusselator how to use real root counting\nalgorithms and graph theoretic tools to efficiently determine the number of\nresonant modes and parameter ranges for stochastic oscillations. We argue that\nstochastic resonance is a network property by showing that resonant modes only\ndepend on the squared Jacobian matrix J2 , unlike deterministic oscillations\nwhich are determined by J. By using graph theoretic tools, analysis of\nstochastic behaviour for larger networks is simplified and chemical reaction\nnetworks with multiple resonant modes can be identified easily.\n