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Published on: June 8, 2018
Collective modes of coupled phase oscillators with delayed coupling.
Saúl Ares1, Luis G Morelli, David J Jörg
1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany.
Physical Review Letters
|September 26, 2012
Summary
Delayed coupling significantly impacts timing and pattern formation in dynamic oscillator systems. Our study reveals how these delays influence collective wave patterns in cellular oscillators, crucial for vertebrate embryo development.
Area of Science:
- Physics
- Biophysics
- Developmental Biology
Background:
- Dynamic oscillators are fundamental to biological and physical systems.
- Pattern formation in biological systems, like the segmentation clock in vertebrate embryos, is critical for development.
- Coupling delays can significantly alter the behavior of oscillatory systems.
Purpose of the Study:
- To investigate the influence of delayed coupling on timing and pattern formation in spatially extended dynamic oscillator systems.
- To develop a continuum theory for collective modes in discrete oscillator lattices.
- To analyze the spatial phase profiles of cellular oscillators within the segmentation clock model.
Main Methods:
- Derivation of a generic continuum theory for collective modes from a discrete lattice of coupled oscillators.
- Application of the continuum theory to analyze spatial phase profiles in cellular oscillators.
- Modeling the interplay of coupling delays and moving boundary conditions.
Main Results:
- Collective wave patterns emerge from the interaction between coupling delays and moving boundary conditions.
- The spatial phase profiles of collective modes are demonstrably dependent on the presence and magnitude of coupling delays.
- A generic continuum theory was successfully derived for long-wavelength collective modes.
Conclusions:
- Coupling delays are a key factor in regulating timing and pattern formation in dynamic oscillator systems.
- The findings provide insights into the mechanisms underlying pattern formation in developmental biology, specifically the segmentation clock.
- The developed continuum theory offers a valuable framework for studying similar spatially extended oscillatory systems.
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