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

Mami Iwata; Shin-ichi Sasa

doi:10.1103/physreve.78.055202

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arXiv · 0806.1096

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

Mami Iwata·Shin-ichi Sasa

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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.

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Mami Iwata, Shin-ichi Sasa. 2008-11-15. Scale-free patterns at a saddle-node bifurcation in a stochastic system. https://doi.org/10.1103/physreve.78.055202

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