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Characterization of the noise effect on weak synchronization.

Sang-Yoon Kim1, Woochang Lim, Alexei Jalnine

  • 1Department of Physics, Kangwon National University, Chunchon, Kangwon-Do 200-701, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
Summary

Noise impacts weak synchronization in coupled 1D maps. A new noise sensitivity exponent (NSE) quantifies this, revealing noise and parameter mismatch have similar effects on characteristic timescales.

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Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Statistical physics

Background:

  • Weak synchronization in coupled chaotic systems is sensitive to perturbations.
  • Characterizing this sensitivity is crucial for understanding system stability.

Purpose of the Study:

  • To investigate the effect of noise on weak synchronization in two coupled identical one-dimensional (1D) maps.
  • To introduce and analyze a quantifier for noise sensitivity.

Main Methods:

  • Analysis of coupled identical 1D maps.
  • Introduction of the noise sensitivity exponent (NSE).
  • Investigation of bounded noise and parameter mismatch effects.

Main Results:

  • Weakly stable synchronous chaotic attractors (SCA) exhibit noise sensitivity due to positive local transverse Lyapunov exponents.

Related Experiment Videos

  • The noise sensitivity exponent (NSE) quantifies this sensitivity.
  • NSE values match the parameter sensitivity exponent for bounded noise.
  • The scaling exponent for time spent near the diagonal is the reciprocal of the NSE for both bubbling and riddling cases.

    • Conclusions:

    • Noise and parameter mismatch exert similar effects on the scaling behavior of average characteristic time in weakly synchronized systems.
    • The NSE provides a quantitative measure for noise sensitivity in such systems.