A Method to Calculate Homoclinic Points of a Two-DimensionaI Noninvertible Map

摘要

A numerical method is presented for calculating transverse and non-transverse (or tangent) types of homoclinic points of a two-dimensional noninvertible map having an invariant set that reduces to a one-dimensional noninvertible map. To illustrate bifurcation diagrams of homoclinic points and transitions of chaotic states near the bifurcation parameter values, three systems including coupled chaotic maps are studied.