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Entropy and bifurcations in a chaotic laser
Pieter Collins1, Bernd Krauskopf
1Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom. pcollins@liv.ac.uk
Summary
Researchers calculated bounds for topological entropy in a semiconductor laser with optical injection. They analyzed chaotic dynamics and boundary crises, finding entropy persists in chaotic saddles post-bifurcation.
Area of Science:
- Nonlinear Dynamics
- Laser Physics
- Chaos Theory
Background:
- Semiconductor lasers with optical injection can exhibit complex chaotic dynamics.
- Understanding the behavior of chaotic attractors is crucial for laser applications.
- Topological entropy quantifies the complexity of chaotic systems.
Purpose of the Study:
- To compute bounds on the topological entropy of a chaotic attractor in a semiconductor laser with optical injection.
- To analyze the global properties of stable and unstable manifolds of periodic points.
- To characterize the boundary crisis leading to the destruction of the chaotic attractor.
Main Methods:
- Utilizing the Poincaré return map to a fixed plane.
- Globally computing stable and unstable manifolds of periodic points.
- Entropy calculations based on information from manifold analysis.
Main Results:
- Bounds on topological entropy were successfully computed.
- The global computation of manifolds was achieved despite challenges with smooth Poincaré maps.
- A boundary crisis involving a periodic point with negative eigenvalues was identified.
- The chaotic attractor was destroyed during this boundary crisis.
Conclusions:
- Topological entropy associated with the chaotic attractor persists in a chaotic saddle after the bifurcation.
- The study provides a method for analyzing chaotic systems where global Poincaré maps are not smoothly defined.
- This research contributes to the understanding of bifurcations and chaos in optically injected semiconductor lasers.
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