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.

• Publication year

  2008

• Venue

  Physical review. E, Statistical, nonlinear, and soft matter physics

• Publication date

  2008-06-06

• Fields of study

  Medicine, Physics, Mathematics

• Identifiers
  DOI 10.1103/PhysRevE.78.055202arXiv 0806.1096PMID 19113177
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• The organizing principles of neuronal avalanches: cell assemblies in the cortex?

  2007cited by this paper
• Inhomogeneous mode-coupling theory and growing dynamic length in supercooled liquids.

  2006cited by this paper
• Non-ergodic transitions in many-body Langevin systems: a method of dynamical system reduction

  2006cited by this paper
• Chemical oscillations

  2006cited by this paper
• A theory for critically divergent fluctuations of dynamical events at non-ergodic transitions

  2006cited by this paper
• Dynamical heterogeneity close to the jamming transition in a sheared granular material.

  2005cited by this paper
• Direct Experimental Evidence of a Growing Length Scale Accompanying the Glass Transition

  2005cited by this paper
• Heterogeneity and growing length scales in the dynamics of kinetically constrained lattice gases in two dimensions.

  2004cited by this paper
• Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition

  2004cited by this paper
• Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell.

  2003cited by this paper
• Asymmetric kinks: stabilization by entropic forces.

  2001cited by this paper
• Three-dimensional direct imaging of structural relaxation near the colloidal glass transition

  2000cited by this paper
• Dynamics of highly supercooled liquids: Heterogeneity, rheology, and diffusion

  1998cited by this paper
• Theory of phase-ordering kinetics

  1993cited by this paper
• Intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators

  1990cited by this paper
• Geometrical cluster growth models and kinetic gelation

  1986cited by this paper
• Chemical Oscillations, Waves, and Turbulence

  1984cited by this paper
• Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

  1983cited by this paper
• Lectures On Phase Transitions And The Renormalization Group

  1972cited by this paper
• Introduction to Phase Transitions and Critical Phenomena

  1972cited by this paper
• Introduction to Phase Transitions and Critical Phenomena

  1972cited by this paper

• Wake-sleep transition as a noisy bifurcation.

  2016cites this paper
• Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation.

  2010cites this paper
• Singular perturbation near mode-coupling transition

  2009cites this paper