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Published on: August 14, 2015
Synchronization in a system of globally coupled oscillators with time delay
1Department of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-742, Korea.
Summary
This study investigates coupled oscillators with time delay, revealing discontinuous transitions and multistability. The findings show how delay impacts synchronization frequency and system behavior.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Oscillator networks
Background:
- Globally coupled oscillators are fundamental models in physics and engineering.
- Time delays in coupling significantly alter system dynamics and synchronization properties.
Purpose of the Study:
- To analyze synchronization phenomena in globally coupled oscillators with time delay.
- To derive and investigate self-consistency equations for the order parameter, considering delay effects.
- To explore the phase diagram and identify transition types and emergent behaviors.
Main Methods:
- Derivation of self-consistency equations for the order parameter.
- Analytical investigation of the derived equations to determine transition types.
- Phase diagram construction based on coupling strength and delay time.
- Numerical simulations to validate analytical findings.
Main Results:
- The system exhibits both continuous and discontinuous transitions between incoherent and coherent states.
- Multistability, with multiple coexisting coherent states, is a ubiquitous phenomenon.
- Time delay can lead to the suppression of synchronization frequency.
- The phase diagram clearly illustrates the regions of different synchronization behaviors.
Conclusions:
- Time delay introduces complex dynamics, including discontinuous transitions and multistability, in coupled oscillator systems.
- The synchronization frequency is sensitive to the delay time, potentially being suppressed.
- Understanding these phenomena is crucial for designing and controlling complex networks with delayed interactions.
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