  We study the dynamics of inertial particles in two dimensional incompressible
flows. The particle dynamics is modelled by four dimensional dissipative
bailout embedding maps of the base flow which is represented by 2-d area
preserving maps. The phase diagram of the embedded map is rich and interesting
both in the aerosol regime, where the density of the particle is larger than
that of the base flow, as well as the bubble regime, where the particle density
is less than that of the base flow. The embedding map shows three types of
dynamic behaviour, periodic orbits, chaotic structures and mixed regions. Thus,
the embedding map can target periodic orbits as well as chaotic structures in
both the aerosol and bubble regimes at certain values of the dissipation
parameter. The bifurcation diagram of the 4-d map is useful for the
identification of regimes where such structures can be found. An attractor
merging and widening crisis is seen for a special region for the aerosols. At
the crisis, two period-10 attractors merge and widen simultaneously into a
single chaotic attractor. Crisis induced intermittency is seen at some points
in the phase diagram. The characteristic times before bursts at the crisis show
power law behaviour as functions of the dissipation parameter. Although the
bifurcation diagram for the bubbles looks similar to that of aerosols, no such
crisis regime is seen for the bubbles. Our results can have implications for
the dynamics of impurities in diverse application contexts.
