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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

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

Mami Iwata1, Shin-Ichi Sasa

  • 1Department 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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2008
PubMed
Summary
This summary is machine-generated.

Scale-free patterns emerge in stochastic systems near saddle-node bifurcations. These patterns appear during relaxation processes, characterized by exiting times from a marginal saddle point.

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Area of Science:

  • Physics
  • Complex Systems
  • Nonlinear Dynamics

Background:

  • Spatially extended stochastic systems exhibit complex behaviors.
  • Bifurcations, such as the saddle-node bifurcation, are critical points where system dynamics change qualitatively.
  • Understanding pattern formation in such systems is crucial for various scientific fields.

Purpose of the Study:

  • To investigate the emergence of scale-free patterns in a stochastic system undergoing a saddle-node bifurcation.
  • To characterize the nature of these scale-free patterns and their temporal appearance.
  • To determine the critical exponents associated with these patterns.

Main Methods:

  • Simulation of a spatially extended stochastic system.
  • Analysis of relaxation processes from a spatially homogeneous initial condition.
  • Characterization of scale-free patterns using the spatial configuration of exiting times from a marginal saddle.

Main Results:

  • Scale-free patterns were observed in the stochastic system.
  • These patterns were found to appear at a specific time during relaxation.
  • The scale-free nature was linked to the exiting time dynamics at a marginal saddle point.
  • Critical exponents were determined through numerical experiments.

Conclusions:

  • Saddle-node bifurcations in spatially extended stochastic systems can lead to scale-free patterns.
  • The emergence of these patterns is a transient phenomenon during relaxation.
  • The spatial configuration of exiting times provides a characterization of scale-free behavior.