TY - JOUR
T1 - Acumulating regions of winding periodic orbits in optically driven lasers
AU - Krauskopf, B.
AU - Wieczorek, S.
PY - 2002
Y1 - 2002
N2 - We investigate the route to locking in class B lasers subject to optically injected light for injection strengths and detunings near a codimension-two saddle-node Hopf point. This is the parameter region where the Adler approximation is not valid and where Yeung and Strogatz recently reported a self-similar cascade of periodic orbits in the case of a solid-state laser. We explain this cascade as an accumulation of large regions bounded by saddle-node bifurcations of periodic orbits, but also containing further bifurcations, such as period-doubling, torus bifurcations and small pockets of chaos. In the vicinity of the simultaneous saddle-node and Hopf bifurcations, successive periodic orbits wind more and more near the point in phase space where the saddle-node bifurcation is about to occur. This leads to a self-similar period-adding cascade. By varying the linewidth enhancement parameter α from zero, the case of a solid-state or CO
AB - We investigate the route to locking in class B lasers subject to optically injected light for injection strengths and detunings near a codimension-two saddle-node Hopf point. This is the parameter region where the Adler approximation is not valid and where Yeung and Strogatz recently reported a self-similar cascade of periodic orbits in the case of a solid-state laser. We explain this cascade as an accumulation of large regions bounded by saddle-node bifurcations of periodic orbits, but also containing further bifurcations, such as period-doubling, torus bifurcations and small pockets of chaos. In the vicinity of the simultaneous saddle-node and Hopf bifurcations, successive periodic orbits wind more and more near the point in phase space where the saddle-node bifurcation is about to occur. This leads to a self-similar period-adding cascade. By varying the linewidth enhancement parameter α from zero, the case of a solid-state or CO
U2 - 10.1016/S0167-2789(02)00650-4
DO - 10.1016/S0167-2789(02)00650-4
M3 - Article
SN - 0167-2789
JO - Physica D. Nonlinear Phenomena
JF - Physica D. Nonlinear Phenomena
ER -