Stochastic Analysis of Limit Cycle Behavior in Spatially Extended Systems
- 12 August 1996
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 77 (7) , 1398-1401
- https://doi.org/10.1103/physrevlett.77.1398
Abstract
The statistical properties of a one-dimensional reaction-diffusion system undergoing a Hopf bifurcation are studied using the master equation approach. The analysis reveals nontrivial interferences between macroscopic dynamics and mesoscopic local fluctuations that eventually wipe out any trace of homogeneous oscillations, even though the latter are asymptotically stable solutions of the deterministic equations.Keywords
This publication has 8 references indexed in Scilit:
- Breakdown of global coupling in oscillatory chemical reactionsThe Journal of Chemical Physics, 1993
- Normal form of stochastic equations for chemical systems near bifurcation pointsPhysics Letters A, 1991
- Steady-state ensemble for the complex Ginzburg-Landau equation with weak noisePhysical Review A, 1990
- Nonequilibrium statistical mechanics model showing self-sustained oscillationsPhysical Review Letters, 1988
- Nonequilibrium Phase Transitions and Chemical InstabilitiesAdvances in Chemical Physics, 1982
- Systematic analysis of the multivariate master equation for a reaction-diffusion systemJournal of Statistical Physics, 1980
- Renormalization group approach to chemical instabilitiesZeitschrift für Physik B Condensed Matter, 1977
- Langevin forces in chemically reacting multicomponent fluidsThe Journal of Chemical Physics, 1976