A method to calculate basin bifurcation sets for a two-dimensional noninvertible map

For models in the form of noninvertible maps we propose a numerical method to calculate a class of basin bifurcation sets in a parameter space. It is known that basin bifurcations may result from the contact of a basin bounda ry with the critical curve (locus of points having two coincident rank-one preimages) segment. Therefore, when the map is smooth, we propose the metho d to obtain the tangent points of a basin boundary (stable set of saddle ty pe periodic points) and a critical curve. Numerical examples for a two-dime nsional quadratic noninvertible map are illustrated and new results of basi n bifurcations are shown.