Contact Bifurcations in Two-Dimensional Endomorphisms Related with Homoclinic or Heteroclinic Orbits

M.R. Ferchichi1, I.Djellit2, J.C. Sprott3

1,2Laboratoire Math´ematiques, Dynamique et Mod´elisation, University of Annaba - Faculty of Sciences, Department of
Mathematics - P.B.12- 23000 Annaba , Algeria
3University of Wisconsin, Department of Physics - Madison, WI 53706 USA

(Received 9 June 2010, accepted 30 August 2010)


In this paper we show the homoclinic bifurcations which are involved in some contact bifurcations of basins of attraction in noninvertible two-dimensional map. That is, we are interested in the link between contact bifurcations of a chaotic area and homoclinic bifurcations of a saddle point or of an expanding fixed point located on the boundary of the basin of attraction of the chaotic area. We shall analyze the particular
case of a map having up to three distinct preimages, and the basins’s bifurcations are investigated by use of the technique of critical curves.

Ref: M. R. Ferchichi, I. Djellit, and J. C. Sprott, International Journal of Nonlinear Science 10, 484-494 (2010)

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