The occurrence of riddled basins and blowout bifurcations in a parametric nonlinear system

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