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Related Experiment Video

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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-flip transition in relay-coupled nonlinear oscillators.

Amit Sharma¹, Manish Dev Shrimali, Awadhesh Prasad

¹The LNM Institute of Information Technology, Jaipur, India.

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

|August 27, 2011

Summary

Relay-coupled oscillators without time delay exhibit phase-flip transitions due to conjugate variable coupling. This transition shows bistability and leads to amplitude death, unlike abrupt transitions seen with time delays.

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Area of Science:

Nonlinear Dynamics
Complex Systems
Coupled Oscillators

Background:

Coupled oscillators often exhibit phase transitions influenced by time delays.
Relay coupling introduces an intermediary oscillator in the interaction pathway.

Purpose of the Study:

Investigate phase-flip transitions in relay-coupled oscillators without time delay.
Characterize the dynamics, including bistability and amplitude death, in this system.

Main Methods:

Analysis of coupled Rössler-like oscillators.
Examination of average phase difference and Lyapunov exponents.
Numerical simulations to observe system behavior.

Main Results:

Phase-flip transition observed without time delay via conjugate variable coupling.
A parameter region of bistability identified, where in-phase and out-of-phase oscillations coexist.
Transitions to amplitude death and fixed-point stabilization observed with increased coupling strength.

Conclusions:

Relay coupling through conjugate variables can induce phase-flip transitions without time delay.
Bistability and amplitude death are key emergent phenomena in this coupling scheme.
The findings offer insights into complex dynamics in coupled oscillatory systems.