A METHOD TO CALCULATE BASIN BIFURCATION SETS FOR A TWO-DIMENSIONAL NONINVERTIBLE MAP

Abstract

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 boundary with the critical curve (locus of points having two coincident rank-one preimages) segment. Therefore, when the map is smooth, we propose the method to obtain the tangent points of a basin boundary (stable set of saddle type periodic points) and a critical curve. Numerical examples for a two-dimensional quadratic noninvertible map are illustrated and new results of basin bifurcations are shown.