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Rare events in mixed-mode oscillations from weakly coupled lasers
Eusebius J Doedel1, Carlos L Pando L2
1Department of Computer Science, Concordia University, Montréal, Québec H3G 1M8, Canada.
Physical Review. E
|December 25, 2019
Summary
Coupled molecular lasers exhibit rare, low-amplitude events under specific conditions. Breaking symmetry can lead to extreme rogue waves, deviating from standard statistical distributions.
Area of Science:
- Nonlinear dynamics
- Laser physics
- Computational neuroscience
Background:
- Mutually coupled molecular lasers can exhibit complex behaviors like mixed-mode oscillations and chaos.
- Inhibitory nonlinear coupling, seen in these lasers, is also relevant to biological systems like neuron models.
Purpose of the Study:
- Investigate rare event generation in coupled molecular laser systems.
- Analyze the influence of coupling strength and symmetry on event characteristics.
- Characterize extreme rare events, including rogue waves and dragon kings.
Main Methods:
- Extensive numerical bifurcation analysis.
- Numerical simulations of the coupled laser system.
- Statistical analysis of event distributions.
Main Results:
- Symmetric configurations with small coupling generate rare events with very small amplitudes due to resonances.
- Breaking system symmetry near a Hopf bifurcation leads to extreme rare events (rogue waves) in one laser.
- These extreme events deviate from power-law distributions, resembling dragon kings.
Conclusions:
- Rare events in coupled nonlinear systems are sensitive to coupling parameters and system symmetry.
- The study identifies conditions for generating both low-amplitude rare events and extreme rogue waves.
- Findings offer insights into the statistical properties and origins of extreme events in dynamical systems.
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