Non-meanfield deterministic limits in chemical reaction kinetics.

A general mechanism is proposed by which small intrinsic fluctuations in a system far from equilibrium can result in nearly deterministic dynamical behaviors which are markedly distinct from those realized in the meanfield limit. The mechanism is demonstrated for the kinetic Monte Carlo version of the Schnakenberg reaction where we identified a scaling limit in which the global deterministic bifurcation picture is fundamentally altered by fluctuations. Numerical simulations of the model are found to be in quantitative agreement with theoretical predictions.

[1]  E Weinan,et al.  Self-induced stochastic resonance in excitable systems , 2005 .

[2]  D. Gillespie.  A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .

[3]  J. White,et al.  Channel noise in neurons , 2000, Trends in Neurosciences.

[4]  Eric Vanden-Eijnden,et al.  Two distinct mechanisms of coherence in randomly perturbed dynamical systems. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Adam Shwartz,et al.  Large Deviations For Performance Analysis , 2019 .

[6]  C. Gardiner.  Handbook of Stochastic Methods , 1983 .

[7]  Daniel T. Gillespie,et al.  Concerning the validity of the stochastic approach to chemical kinetics , 1977 .

[8]  J. Schnakenberg,et al.  Simple chemical reaction systems with limit cycle behaviour. , 1979, Journal of theoretical biology.

[9]  A. Goldbeter,et al.  Biochemical Oscillations And Cellular Rhythms: Contents , 1996 .

[10]  Mark Freidlin,et al.  On Stable Oscillations and Equilibriums Induced by Small Noise , 2001 .

[11]  J. García-Ojalvo,et al.  Effects of noise in excitable systems , 2004 .

[12]  P. Hänggi,et al.  Reaction-rate theory: fifty years after Kramers , 1990 .

[13]  J. Paulsson.  Summing up the noise in gene networks , 2004, Nature.

[14]  M. Freidlin,et al.  Random Perturbations of Dynamical Systems , 1984 .

[15]  Mark Freidlin,et al.  Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point , 1998 .

[16]  Michel Mandjes,et al.  Large Deviations for Performance Analysis: Queues, Communications, and Computing , Adam Shwartz and Alan Weiss (New York: Chapman and Hall, 1995). , 1996, Probability in the Engineering and Informational Sciences.

[17]  Mark Freidlin,et al.  ON STOCHASTIC PERTURBATIONS OF DYNAMICAL SYSTEMS WITH FAST AND SLOW COMPONENTS , 2001 .

[18]  J. Schnakenberg.  Network theory of microscopic and macroscopic behavior of master equation systems , 1976 .

[19]  J. Kurths,et al.  Coherence Resonance in a Noise-Driven Excitable System , 1997 .

[20]  S. Leibler,et al.  Mechanisms of noise-resistance in genetic oscillators , 2002, Proceedings of the National Academy of Sciences of the United States of America.