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

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Published on: May 30, 2014

Amplitude death in nonlinear oscillators with nonlinear coupling.

Awadhesh Prasad¹, Mukeshwar Dhamala, Bhim Mani Adhikari

¹Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India.

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

|April 7, 2010

Summary

Amplitude death, the cessation of oscillations in coupled nonlinear systems, is a general phenomenon. It occurs in various systems, including model neurons and Rössler oscillators, and can be controlled by designing nonlinear coupling.

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Area of Science:

Physics
Dynamical Systems
Neuroscience

Background:

Amplitude death is a phenomenon in coupled nonlinear systems where oscillations cease due to stabilized fixed points.
This phenomenon has been observed in various coupled oscillatory systems.

Purpose of the Study:

To demonstrate the generality of amplitude death in nonlinearly coupled systems.
To explore the role of parameter mismatch and time delays in amplitude death.
To show that arbitrary steady states can be stabilized by designing nonlinear coupling.

Main Methods:

Investigated amplitude death in nonlinearly coupled systems.
Analyzed the impact of parameter mismatch and time delays.
Applied the concept to synaptically coupled model neurons and Rössler oscillators.
Studied networks of nonlinear oscillators with nonlinear coupling.

Main Results:

Amplitude death is a general phenomenon in nonlinearly coupled systems, occurring even without parameter mismatch or time delay.
Time-delayed interactions can enhance the effect of amplitude death.
The study successfully applied amplitude death to model neurons and Rössler oscillators.
Arbitrary steady states can be stabilized by carefully designing the nonlinear coupling.

Conclusions:

Amplitude death is a widespread phenomenon in coupled nonlinear dynamics.
Nonlinear coupling offers a versatile mechanism for controlling system dynamics, enabling stabilization of desired steady states.
The findings have implications for understanding and controlling complex systems like neural networks and oscillator networks.