591 research outputs found
Delay-induced multistability near a global bifurcation
We study the effect of a time-delayed feedback within a generic model for a
saddle-node bifurcation on a limit cycle. Without delay the only attractor
below this global bifurcation is a stable node. Delay renders the phase space
infinite-dimensional and creates multistability of periodic orbits and the
fixed point. Homoclinic bifurcations, period-doubling and saddle-node
bifurcations of limit cycles are found in accordance with Shilnikov's theorems.Comment: Int. J. Bif. Chaos (2007), in prin
Drifting instabilities of cavity solitons in vertical cavity surface-emitting lasers with frequency selective feedback
In this paper we study the formation and dynamics of self-propelled cavity
solitons (CSs) in a model for vertical cavity surface-emitting lasers (VCSELs)
subjected to external frequency selective feedback (FSF), and build their
bifurcation diagram for the case where carrier dynamics is eliminated. For low
pump currents, we find that they emerge from the modulational instability point
of the trivial solution, where traveling waves with a critical wavenumber are
formed. For large currents, the branch of self-propelled solitons merges with
the branch of resting solitons via a pitchfork bifurcation. We also show that a
feedback phase variation of 2\pi can transform a CS (whether resting or moving)
into a different one associated to an adjacent longitudinal external cavity
mode. Finally, we investigate the influence of the carrier dynamics, relevant
for VCSELs. We find and analyze qualitative changes in the stability properties
of resting CSs when increasing the carrier relaxation time. In addition to a
drifting instability of resting CSs, a new kind of instability appears for
certain ranges of carrier lifetime, leading to a swinging motion of the CS
center position. Furthermore, for carrier relaxation times typical of VCSELs
the system can display multistability of CSs.Comment: 11 pages, 12 figure
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