Effect of focusing and caustics on exit phenomena in systems lacking detailed balance
Abstract
We study the trajectories followed by a particle weakly perturbed by noise, when escaping from the domain of attraction of a stable fixed point. If the particle's stationary distribution lacks detailed balance, a focus may occur along the most probable exit path, leading to a breakdown of symmetry (if present). The exit trajectory bifurcates, and the exit location distribution may become ``skewed'' (non-Gaussian). The weak-noise asymptotics of the mean escape time are also affected. Our methods extend to the study of skewed exit location distributions in stochastic models without symmetry.
- Publication:
-
Physical Review Letters
- Pub Date:
- September 1993
- DOI:
- 10.1103/PhysRevLett.71.1783
- arXiv:
- arXiv:chao-dyn/9305010
- Bibcode:
- 1993PhRvL..71.1783M
- Keywords:
-
- 05.40.+j;
- 02.50.-r;
- Probability theory stochastic processes and statistics;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- REVTEX macros (latest version). Two accompanying PS figures, one of which is large (over 600K unpacked)