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Delay-induced patterns in a two-dimensional lattice of coupled oscillators
Markus Kantner1, Eckehard Schöll2, Serhiy Yanchuk1
1Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany.
Scientific Reports
|February 18, 2015
Summary
Stable spatio-temporal patterns emerge in 2D lattices of coupled oscillators with varied coupling delays. A novel "hybrid dispersion relation" method analyzes pattern stability in these complex systems.
Area of Science:
- Physics
- Dynamical Systems
- Computational Neuroscience
Background:
- Coupled oscillator networks are fundamental to understanding complex phenomena.
- Non-homogeneous coupling delays introduce significant challenges in predicting system behavior.
- Spatio-temporal pattern formation is a key area of research in nonlinear dynamics.
Purpose of the Study:
- To demonstrate the creation of stable spatio-temporal periodic patterns in 2D lattices of coupled oscillators.
- To investigate the role of non-homogeneous coupling delays in pattern formation.
- To introduce a new analytical tool for stability analysis in delayed systems.
Main Methods:
- Utilized 2D lattices of coupled oscillators.
- Employed FitzHugh-Nagumo and Stuart-Landau oscillator models.
- Introduced and applied a
- hybrid dispersion relation
- for stability analysis.
Main Results:
- Successfully generated diverse stable spatio-temporal periodic patterns.
- Demonstrated the influence of non-homogeneous coupling delays on pattern characteristics.
- Validated the effectiveness of the hybrid dispersion relation in predicting pattern stability.
Conclusions:
- Non-homogeneous coupling delays can be harnessed to create predictable spatio-temporal patterns.
- The hybrid dispersion relation provides a powerful framework for analyzing stability in delayed oscillator networks.
- This work offers insights into pattern formation relevant to neural networks and other complex systems.
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