Scale-free patterns at a saddle-node bifurcation in a stochastic system

2008/06/30 by Mami Iwata, Shin‐ichi Sasa, Shin-ichi Sasa · 4 citations
Computer Science · Environmental Science · Mathematics · Physics and Astronomy · #Bifurcation #Bifurcation theory #Ecosystem dynamics and resilience #Geometry #Infinite-period bifurcation #Mathematical optimization #Mathematics #Node (physics) #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Physics #Quantum mechanics #Saddle #Saddle point #Saddle-node bifurcation #Scale (ratio) #Statistical physics #cond-mat.stat-mech #stochastic dynamics and bifurcation

paper · pdf · doi:10.1103/physreve.78.055202

published in Physical Review E 78(5), 055202 (American Physical Society) · 4 pages, 6 figures

openalex publication_date 2008/11/14 · arxiv created 2008/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• Lectures on Phase Transitions and the Renormalization Group
• Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition
• Intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators
• Dynamical Heterogeneity Close to the Jamming Transition in a Sheared Granular Material