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

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

2008-06-06

arxiv.org/abs/0806.1096v2

Phys. Rev. E 78, 055202(R) (2008)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 6 figures

Scientific paper

10.1103/PhysRevE.78.055202

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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