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Published on: March 25, 2014
Stimulus-locked responses of two phase oscillators coupled with delayed feedback
Valerii Krachkovskyi1, Oleksandr V Popovych, Peter A Tass
1Institute of Medicine and Virtual Institute of Neuromodulation, Research Centre Jülich, 52425 Jülich, Germany.
Summary
Pulsatile stimulation can control coupled phase-locked loops (PLLs) by inducing transient or long-lasting changes in their dynamics. Appropriately calibrated stimuli can shift systems between synchronized and desynchronized states, offering potential physical and medical applications.
Area of Science:
- Nonlinear Dynamics
- Complex Systems
Background:
- Studies coupled phase-locked loops (PLLs) with internal delays.
- Investigates dynamics arising from delayed self-feedback.
Purpose of the Study:
- Examines the impact of pulsatile stimulation on coupled PLLs.
- Analyzes stimulus-locked responses across various dynamical regimes.
Main Methods:
- Simulates a system of two coupled PLLs with delayed self-feedback.
- Applies pulsatile stimulation to both oscillators.
Main Results:
- Delayed feedback yields diverse dynamics: phase-locking, chaos, and desynchronization.
- Stimuli can induce phase resets, response clustering, and long resynchronization.
- Maximal perturbation occurs when stimuli trap the system near saddle fixed points.
- Single stimuli can switch systems between synchronized and desynchronized states.
Conclusions:
- Calibrated pulse stimuli can significantly alter oscillator dynamics.
- Pulse stimulation offers an effective method for controlling coupled oscillators.
- Findings have potential relevance in physical and medical applications.
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