ON SOME GLOBAL BIFURCATIONS OF THE DOMAINS OF FEASIBLE TRAJECTORIES: AN ANALYSIS OF RECURRENCE EQUATIONS

Abstract

This paper is an attempt to give new results, by a computer-assisted study, on some global bifurcations that change the structure of the domain of feasible trajectories (bounded discrete trajectories having an ecological sense) which can be obtained by the union of all rank preimages of axes. Three two-dimensional recurrence equations (or maps) are analyzed. The two first maps are degenerated invertible maps (i.e. the inverses of them are well defined except a set of zero lebergue measure) for which the basins of attractor are obtained by the backward iteration of a stable manifold of a saddle fixed point belonging to the basin boundary, and the interior domains of feasible trajectories are given by the intersection between the basin of attractor and the first quadrant. The other is a noninvertible map which is investigated by the use of critical curves, a powerful tool for the analysis of global properties of two-dimensional maps.