## Abstract

Boundary crisis is a mechanism for destroying a chaotic attractor when one parameter is varied. In a two-parameter setting the locus of boundary crisis is associated with curves of homo- or heteroclinic tangency bifurcations of saddle periodic orbits. It is known that the locus of boundary crisis contains many gaps, corresponding to channels
(regions of positive measure) where a non-chaotic attractor persists.
One side of such a subduction channel is a saddle-node bifurcation of
a periodic orbit that marks the start of a periodic window in the
chaotic regime; the other side of the channel is formed by a homo- or
heteroclinic tangency bifurcation associated with this diffferent
saddle periodic orbit. We present a two-parameter study of boundary
crisis in the Ikeda map, which models the dynamics of energy levels in
a laser ring cavity. We confirm the existence of many gaps on the
boundary-crisis locus. However, the gaps correspond to subduction
channels that can have a rather different structure compared to what
is known in the literature.

Original language | English |
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Publication status | Published - Jul 2010 |