Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation.
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.
Iwata
Mami
M
Department of Pure and Applied Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan. iwata@jiro.c.u-tokyo.ac.jp
Sasa
Shin-ichi
S