Entropy and bifurcations in a chaotic laser.
We compute bounds on the topological entropy associated with a chaotic attractor of a semiconductor laser with optical injection. We consider the Poincaré return map to a fixed plane, and are able to compute the stable and unstable manifolds of periodic points globally, even though it is impossible to find a plane on which the Poincaré map is globally smoothly defined. In this way, we obtain the information that forms the input of the entropy calculations, and characterize the boundary crisis in which the chaotic attractor is destroyed. This boundary crisis involves a periodic point with negative eigenvalues, and the entropy associated with the chaotic attractor persists in a chaotic saddle after the bifurcation.
Collins
Pieter
P
Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom. pcollins@liv.ac.uk
Krauskopf
Bernd
B