Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation
Abstract
A Langevin equation whose deterministic part undergoes a saddle-node bifurcation is investigated theoretically. It is found that statistical properties of relaxation trajectories in this system exhibit divergent behaviors near a saddle-node bifurcation point in the weak-noise limit, while the final value of the deterministic solution changes discontinuously at the point. A systematic formulation for analyzing a path probability measure is constructed on the basis of a singular perturbation method. In this formulation, the critical nature turns out to originate from the neutrality of exiting time from a saddle-point. The theoretical calculation explains results of numerical simulations.
Keywords
Cite
@article{arxiv.1002.4239,
title = {Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation},
author = {Mami Iwata and Shin-ichi Sasa},
journal= {arXiv preprint arXiv:1002.4239},
year = {2015}
}
Comments
18pages, 17figures.The version 2, in which minor errors have been fixed, will be published in Phys. Rev. E