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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Published on: May 30, 2014

Phase-locking swallows in coupled oscillators with delayed feedback.

Oleksandr V Popovych¹, Valerii Krachkovskyi, Peter A Tass

¹Institute of Neuroscience and Medicine-Neuromodulation (INM-7), Research Center Jülich, 52425 Jülich, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|January 15, 2011

Summary

This summary is machine-generated.

We reveal how delayed feedback in coupled oscillators creates synchronization, including chaotic states. New torus bifurcations alter synchronization patterns, impacting spatial organization and offering analytical insights into system behavior.

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Area of Science:

Nonlinear dynamics
Complex systems
Synchronization phenomena

Background:

Coupled oscillators exhibit complex behaviors, including synchronization.
Delayed feedback is a crucial factor influencing system dynamics.
Previous studies identified specific parameter regions (swallows/shrimps) for phase-locked states.

Purpose of the Study:

To investigate the effects of nonlinear coupling with delayed feedback on limit-cycle oscillators.
To characterize different synchronization states, including phase-locked, modulated, and chaotic.
To explore novel bifurcation scenarios within synchronization regions.

Main Methods:

Analysis of nonlinear coupling between two limit-cycle oscillators with delayed feedback.
Identification and characterization of parameter regions corresponding to various synchronization states.
Investigation of bifurcation mechanisms, specifically comparing torus bifurcations with period-doubling.

Main Results:

Nonlinear coupling with delayed feedback can induce phase-locked, modulated, and chaotic phase synchronization, alongside desynchronization.
Stable phase-locked states form characteristic swallow or shrimp regions in parameter space.
A torus bifurcation scenario for periodic orbits within swallow regions was identified, differing from prior period-doubling findings.
The spatial organization of swallow regions is impacted by this new bifurcation scenario.
The synchronization domain is influenced by swallow regions, with an analytical approximation of the synchronization threshold provided.

Conclusions:

Delayed feedback in coupled oscillators leads to diverse synchronization patterns and novel bifurcation dynamics.
The discovery of torus bifurcations in swallow regions refines our understanding of synchronization phenomena in nonlinear systems.
Analytical approximation of the synchronization threshold offers predictive capabilities for coupled oscillator systems.