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Coupling regularizes individual units in noisy populations.

Cheng Ly1, G Bard Ermentrout

  • 1Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA. chengly@math.pitt.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

Coupling noisy systems can surprisingly regularize individual components, even when connected to more erratic ones. This finding highlights the beneficial impact of network connectivity on system variability.

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Area of Science:

  • Computational neuroscience
  • Nonlinear dynamics
  • Complex systems

Background:

  • Network coupling typically reduces overall system variability.
  • Individual component regularity is crucial in biological systems, especially for specialized cells.
  • The effect of coupling on individual component noise levels is not fully understood.

Purpose of the Study:

  • To investigate how coupling affects the regularity of individual components in noisy systems.
  • To determine if coupling can regularize individual oscillators, even when connected to noisier counterparts.
  • To explore the generalizability of this regularizing effect across different types of noisy oscillators.

Main Methods:

  • Analysis of coupled Ornstein-Uhlenbeck (O-U) processes.
  • Derivation of an asymptotic formula for the variance of the period in weakly coupled noisy oscillators.
  • Application of coupling to higher-dimensional models like Morris-Lecar and Brusselator oscillators.

Main Results:

  • Diffusive coupling regularizes individual Ornstein-Uhlenbeck processes, even when coupled to noisier systems.
  • The regularizing effect of coupling extends to general nonlinear noisy oscillators and is robust to different coupling types.
  • An asymptotic formula accurately predicts the reduction in period variability due to coupling.
  • Reciprocal coupling regularizes individual higher-dimensional oscillators (Morris-Lecar, Brusselator) even when paired with noisier oscillators.

Conclusions:

  • Coupling can have a counterintuitive, beneficial effect by regularizing individual components in noisy systems.
  • Connectivity plays a significant role in modulating the variability of individual oscillators.
  • These findings have implications for understanding biological networks and signal processing in noisy environments.