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Updated: Jun 14, 2026
10:10
Analyzing the Size, Shape, and Directionality of Networks of Coupled Astrocytes
Published on: October 4, 2018
Delay-induced spatial correlations in one-dimensional stochastic networks with nearest-neighbor coupling
Andrey Pototsky1, Natalia B Janson
1Department of Mathematical Sciences, Loughborough University, Leicestershire, United Kingdom.
Summary
Time delays in coupled oscillator networks create multiple wave modes. Noise in these systems induces spatiotemporal fluctuations, influenced by time delay and noise correlation.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Network science
Background:
- Coupled oscillator networks are fundamental in various scientific domains.
- Understanding the influence of time delays and noise is crucial for predicting network behavior.
Purpose of the Study:
- To analyze wave propagation in deterministic oscillator networks with time delays.
- To investigate the response of noisy oscillator networks to external forcing.
Main Methods:
- Analytical computation of neutral modes and their properties (wave numbers, group velocities).
- Characterization of spatiotemporal fluctuations using structure functions in noisy systems.
Main Results:
- Time delay in deterministic systems leads to multiple neutral modes with distinct wave numbers and group velocities.
- Noise induces spatiotemporal fluctuations below the instability threshold, with analytical structure function expressions derived.
- Demonstrated the impact of time delay and noise correlation length on the dominant wave number.
Conclusions:
- Time delays introduce rich dynamics in wave propagation within coupled oscillator networks.
- Noise significantly affects network behavior, leading to fluctuations whose characteristics depend on system parameters and noise properties.
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