On the Poincaré–Hill cycle map of rotational random walk: locating the stochastic limit cycle in a reversible Schnakenberg model

DOI10.1098/rspa.2009.0346zbMath1195.82049OpenAlexW2159784215MaRDI QIDQ4931027

Hong Qian, Melissa Vellela

Publication date: 2 October 2010

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2009.0346

zbMATH Keywords

oscillationPoincaré mapcycle fluxstochastic limit cycle

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05)

Related Items (3)

Cellular biology in terms of stochastic nonlinear biochemical dynamics: Emergent properties, isogenetic variations and chemical system inheritability ⋮ Discretization, bifurcation analysis and chaos control for Schnakenberg model ⋮ Landscapes of non-gradient dynamics without detailed balance: Stable limit cycles and multiple attractors

Cites Work

• Synchronized dynamics and non-equilibrium steady states in a stochastic yeast cell-cycle net\-work
• Concentration fluctuations in a mesoscopic oscillating chemical reaction system

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