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Echo phenomena in large systems of coupled oscillators.
Edward Ott1, John H Platig, Thomas M Antonsen
1Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.
Chaos (Woodbury, N.Y.)
|December 3, 2008
Summary
Systems of coupled oscillators can exhibit "echo" phenomena below a critical coupling strength. Two stimuli separated by time τ can generate spontaneous response pulses at multiples of τ, revealing underlying dynamics.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Statistical physics
Background:
- Large systems of coupled oscillators, like those described by the Kuramoto model, can transition to phase coherence.
- This phase coherence transition is dependent on the coupling strength between oscillators.
Purpose of the Study:
- To investigate phenomena occurring in coupled oscillator systems below the critical coupling strength for phase coherence.
- To analyze the
- echo
- phenomenon in these systems.
Main Methods:
- Theoretical analysis of coupled oscillator dynamics.
- Numerical simulations to illustrate the echo effect.
Main Results:
- Identified
- echo
- phenomena in systems below critical coupling.
- Demonstrated that two successive pulses separated by time τ can induce response pulses at τ, 2τ, 3τ, ... after the second pulse.
Conclusions:
- Echo phenomena provide insights into the dynamics of coupled oscillators below the coherence transition.
- Potential applications of echo phenomena in understanding and controlling complex oscillatory systems.
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