In this paper, a parameter family of maps of the plane living two different lines invariant is stuedid. Our model is a generalization of piecewise linear model defined by Ott et al. [4]. to a nonlinear system. We verify the local dynamic stability of the chaotic attractors using normal Lyapunov exponents. By varying the parameter, we show the occurrence of riddled basin and hysteretic blowout bifurcation. It is shown that the system presents a complex fractal boundary between the initial conditions leading to each of the two attractors. To verify the occurrence of riddled basin, we conjugate our system to a random walk model and using properties of this model we describe riddled basin and blowout in detail. Numerical simulations are presented graphically to confirm the validity of our results.

Keywords