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Journal of Mathematical Chemistry

, Volume 51, Issue 5, pp 1343–1375 | Cite as

Bistable stochastic biochemical networks: highly specific systems with few chemicals

  • Hyung Ju HwangEmail author
  • Juan J. L. Velázquez
Original Paper

Abstract

In this paper we describe a class of stochastic biochemical systems exhibiting bistable behavior, in the sense that the invariant measure associated to the system is concentrated near two different classes of states of the system. We develop methods that allow us to describe the behavior of the invariant measure in some suitable asymptotic limits, as well as the switching times for the transitions between the states close to each of the states with high probability. Due to the discrete character of the problem, switching times cannot be computed using the classical Kramers’ formula, and alternative methods are required.

Keywords

Stochastic chemical system Bistable behavior Switching times Markov processes 

Notes

Acknowledgments

We would like to thank Seongwon Lee for drawing the diagrams in Sect. 4. H.J.H acknowledges the support by Basic Science Research Program (2010-0008127) and (2012047640) through the National Research Foundation of Korea (NRF). J.J.L.V. acknowledges the support by the grant DGES MTM2010-16467.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsPohang University of Science and TechnologyPohangRepublic of Korea
  2. 2.Institute of Applied MathematicsUniversity of BonnBonnGermany

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