  In this paper, a two parameters family $F_{\beta_1,\beta_2}$ of maps of the
plane living two different subspaces invariant is studied. We observe that, our
model exhibits two chaotic attractors $A_i$, $i=0,1$, lying in these invariant
subspaces and identify the parameters at which $A_i$ has a locally riddled
basin of attraction or becomes a chaotic saddle. Then, the occurrence of
riddled basin in the global sense is investigated in an open region of
$\beta_1\beta_2$-plane. We semi-conjugate our system to a random walk model and
define a fractal boundary which separates the basins of attraction of the two
chaotic attractors, then we describe riddled basin in detail. We show that the
model undergos a sequence of bifurcations: "a blowout bifurcation", "a
bifurcation to normal repulsion" and "a bifurcation by creating a new chaotic
attractor with an intermingled basin". Numerical simulations are presented
graphically to confirm the validity of our results.
