An Interdisciplinary Journal

* 2007, Vol.10, No.4, pp.393-400*

The behavior of the well-known Ikeda map with very weak
dissipation (so called nearly conservative case) is investigated.
The changes in the bifurcation structure of the parameter plane
while decreasing the dissipation are revealed. It is shown that
when the dissipation is very weak the system demonstrates some
"intermediate" type of dynamics combining the peculiarities of
conservative and dissipative dynamics. The correspondence between
the trajectories in the phase space in conservative case and the
transformations of the set of initial conditions in the nearly
conservative case is revealed. The dramatic increase of number of
coexisting low-period attractors and the extraordinary growth of
the transient time while the dissipation decreases have been
revealed. The method of plotting a bifurcation trees for the set
of initial conditions has been used to classify existing
attractors by it's structure. Also it was shown that most of
coexisting attractors are destroyed by rather small external
noise, and the transient time in noisy driven systems increases
still more.

*Key words: *
attractors, multistability, noise

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Last updated: *January 16, 2008*