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

Tetsuya YOSHINAGA  Hiroyuki KITAJIMA  Hiroshi KAWAKAMI  Christian MIRA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A   No.9   pp.1560-1566
Publication Date: 1997/09/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
noninvertible map,  homoclinic point,  bifurcation,  coupled map,  nonlinear problem,  

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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.