On a theory of stability for nonlinear stochastic chemical reaction networks

Journal Article · Thu May 14 04:00:00 EDT 2015 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4919834· OSTI ID:22415757

Smadbeck, Patrick; Kaznessis, Yiannis N. ^[1]

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1. Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Ave. SE, Minneapolis, Minnesota 55455 (United States)

We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms.

• OSTI ID: 22415757
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 18 Vol. 142; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHEMICAL REACTIONS
COMPUTERIZED SIMULATION
CORRELATION FUNCTIONS
DISTURBANCES
EIGENVALUES
EQUATIONS
FLUCTUATIONS
MATRICES
NONLINEAR PROBLEMS
PROBABILITY
RELAXATION
RESPONSE FUNCTIONS
STEADY-STATE CONDITIONS
STOCHASTIC PROCESSES