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On a theory of stability for nonlinear stochastic chemical reaction networks
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See supplementary material at http://dx.doi.org/10.1063/1.4919834
for a detailed derivation of the steady-state Jacobian of the probability distribution moments,JSS
, and for an example. The derivation of correlation functions is also detailed in this material.[Supplementary Material]
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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
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.
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