Unnested islands of period doublings in an injected semiconductor laser - art. no. 056204

We present a theoretical study of unnested period-doubling islands in three -dimensional rate equations modeling a semiconductor laser subject to exter nal optical injection. In this phenomenon successive curves of period doubl ings are not arranged in nicely nested islands, but intersect each other. T his overall structure is globally organized by several codimension-2 bifurc ations, As a consequence. the chaotic region existing inside an unnested is land of period doublings can be entered not only via a period-doubling casc ade but also via the breakup of a torus, and even via the sudden appearance of a chaotic attractor. In order to fully understand these different chaot ic transitions we reveal underlying global bifurcations and we show how the y are connected to codimension-2 bifurcation points. Unnested islands of pe riod doublings appear to be generic and hence must be expected in a large c lass of dynamical systems.