In this paper, a two parameters family Fβ1,β2 of maps of the plane having two different invariant subspaces is studied. We observe that, our model exhibits two chaotic attractors Ai, i = 0, 1, lying in these invariant subspaces and identify the parameters at which Ai 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 β1β2-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 undergoes a sequence of bifurcations: ‘‘a blowout bifurcation’’, ‘‘a bifurcation to normal repulsion\\\\\\\" and ‘‘a bifurcation to emergence a new chaotic attractor with an intermingled basin’’. Numerical simulations are presented graphically to confirm the validity of our results.

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