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Phase-locked regimes in delay-coupled oscillator networks.
Nirmal Punetha1, Awadhesh Prasad1, Ramakrishna Ramaswamy2
1Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India.
Chaos (Woodbury, N.Y.)
|January 3, 2015
Summary
Researchers derived a formula for synchronized oscillator frequencies, revealing distinct phase behaviors. Transitions between these states, like in-phase and mixed-phase, can cause sudden frequency changes in coupled systems.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Network Science
Background:
- Globally coupled oscillators with time delays exhibit complex synchronized dynamics.
- Understanding the relationship between phase behavior and oscillation frequency is crucial.
Purpose of the Study:
- To derive an explicit relation for the frequency of synchronized dynamics in globally coupled oscillators with time delays.
- To analyze different phase behaviors, including in-phase and mixed-phase states.
Main Methods:
- Analytical derivation of frequency relations.
- Numerical simulations of coupled Landau-Stuart, Rössler, and FitzHugh-Nagumo oscillator systems.
Main Results:
- Identified two classes of synchronized solutions: in-phase and mixed-phase (random or splay states).
- In the strong coupling limit, only in-phase synchronization persists.
- Discontinuous frequency changes occur during transitions between different synchronized states.
Conclusions:
- The study provides a framework for understanding frequency selection in coupled oscillator networks.
- Transitions between synchronized states can lead to abrupt changes in system frequency.
- Findings are applicable to various physical and biological systems exhibiting coupled oscillatory behavior.
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