Analysis of synchronization in a slowly changing environment: how slow coupling becomes fast weak coupling
Jonathan J Rubin1, Jonathan E Rubin1, G Bard Ermentrout1
1Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.
Physical Review Letters
|August 29, 2014
Summary
We developed a perturbation method showing that slow dynamic media effectively cause weak coupling in oscillators. This approach explains neuronal asynchrony and explores synchronization in biological systems.
Area of Science:
- Physics
- Biology
- Dynamical Systems
Background:
- Many physical and biological systems involve coupled oscillators.
- Indirect coupling often occurs through a dynamic medium that changes slowly over time.
- Understanding this indirect coupling is crucial for modeling complex systems.
Purpose of the Study:
- To present a novel perturbation method for analyzing systems with indirect coupling through a dynamic medium.
- To demonstrate the equivalence between slow medium dynamics and weak oscillator coupling.
- To apply this method to explain phenomena in neuroscience and systems biology.
Main Methods:
- Utilizing the theory of averaging to find periodic solutions for individual systems.
- Analyzing small fluctuations around the mean to understand inter-system coupling.
- Applying perturbation theory to model the effects of the dynamic medium.
Main Results:
- Established that slow dynamics of a coupling medium are equivalent to weak coupling.
- Explained spike-to-spike asynchrony in bursting neurons coupled via extracellular potassium.
- Explored synchronization dynamics in a quorum sensing model.
Conclusions:
- The developed perturbation method provides a powerful tool for analyzing indirectly coupled oscillators.
- This framework offers insights into neuronal network dynamics and bacterial communication.
- The method simplifies the analysis of complex systems by equating slow medium dynamics to weak coupling.
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