Hamilton-Jacobi method for molecular distribution function in a chemical oscillator

Hiizu Nakanishi, Takahiro Sakaue, Jun'Ichi Wakou

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2 Citations (Scopus)


Using the Hamilton-Jacobi method, we solve chemical Fokker-Planck equations within the Gaussian approximation and obtain a simple and compact formula for a conditional probability distribution. The formula holds in general transient situations, and can be applied not only to a steady state but also to an oscillatory state. By analyzing the long time behavior of the solution in the oscillatory case, we obtain the phase diffusion constant along the periodic orbit and the steady distribution perpendicular to it. A simple method for numerical evaluation of these formulas are devised, and they are compared with Monte Carlo simulations in the case of Brusselator as an example. Some results are shown to be identical to previously obtained expressions.

Original languageEnglish
Article number214105
JournalJournal of Chemical Physics
Issue number21
Publication statusPublished - Dec 7 2013


All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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