Scale-free patterns at a saddle-node bifurcation in a stochastic system.
We demonstrate that scale-free patterns are observed in a spatially extended stochastic system whose deterministic part undergoes a saddle-node bifurcation. Remarkably, the scale-free patterns appear only at a particular time in relaxation processes from a spatially homogeneous initial condition. We characterize the scale-free nature in terms of the spatial configuration of the exiting time from a marginal saddle where the pair annihilation of a saddle and a node occurs at the bifurcation point. Critical exponents associated with the scale-free patterns are determined by numerical experiments.
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