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Fabrication and Testing of Microfluidic Optomechanical Oscillators

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Changing dynamical complexity with time delay in coupled fiber laser oscillators.

Anthony L Franz¹, Rajarshi Roy, Leah B Shaw

¹Department of Physics, University of Maryland, College Park, Maryland 20742, USA.

Physical Review Letters

|October 13, 2007

Summary

We studied coupled systems with delays, finding that short delays reduce complexity. Increasing coupling delay logarithmically increases dynamical complexity in these systems.

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Area of Science:

Nonlinear Dynamics
Complex Systems
Optical Engineering

Background:

Mutually coupled systems exhibit complex behaviors.
Internal and coupling delays significantly influence system dynamics.
Understanding delay effects is crucial for controlling complex systems.

Purpose of the Study:

To investigate the impact of coupling delay on the dynamical complexity of two mutually coupled systems.
To quantify complexity changes across four orders of magnitude of coupling delay.
To analyze the relationship between delay duration and system complexity.

Main Methods:

Karhunen-Loève decomposition applied to spatiotemporal data of fiber laser intensity.
Analysis of eigenvalue spectra and significant orthogonal modes.
Shannon information computed from eigenvalue spectra to quantify complexity.

Main Results:

Dynamical complexity is reduced at short coupling delays.
A logarithmic growth in complexity is observed as coupling delay increases.
Eigenvalue spectra and orthogonal modes reveal changes in system dynamics with delay.

Conclusions:

Coupling delay is a critical parameter influencing the complexity of mutually coupled systems.
Short delays can stabilize systems by reducing complexity.
Longer delays lead to a predictable increase in dynamical complexity.