TY - JOUR
T1 - Escape problem for irreversible systems
AU - Maier, Robert S.
AU - Stein, D. L.
PY - 1993
Y1 - 1993
N2 - The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When this assumption fails many of the results of classical transition-rate theory no longer apply, and no general method exists for computing the weak-noise asymptotic behavior of fundamental quantities such as the mean escape time. In this paper we present a general technique for analyzing the weak-noise limit of a wide range of stochastically perturbed continuous-time nonlinear dynamical systems. We simplify the original problem, which involves solving a partial differential equation, into one in which only ordinary differential equations need be solved. This allows us to resolve some old issues for the case when detailed balance holds. When it does not hold, we show how the formula for the asymptotic behavior of the mean escape time depends on the dynamics of the system along the most probable escape path. We also present results on short-time behavior and discuss the possibility of focusing along the escape path.
AB - The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When this assumption fails many of the results of classical transition-rate theory no longer apply, and no general method exists for computing the weak-noise asymptotic behavior of fundamental quantities such as the mean escape time. In this paper we present a general technique for analyzing the weak-noise limit of a wide range of stochastically perturbed continuous-time nonlinear dynamical systems. We simplify the original problem, which involves solving a partial differential equation, into one in which only ordinary differential equations need be solved. This allows us to resolve some old issues for the case when detailed balance holds. When it does not hold, we show how the formula for the asymptotic behavior of the mean escape time depends on the dynamics of the system along the most probable escape path. We also present results on short-time behavior and discuss the possibility of focusing along the escape path.
UR - http://www.scopus.com/inward/record.url?scp=18144390105&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=18144390105&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.48.931
DO - 10.1103/PhysRevE.48.931
M3 - Article
AN - SCOPUS:18144390105
SN - 1063-651X
VL - 48
SP - 931
EP - 938
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 2
ER -