Bifurcations of homoclinic orbits in bimodal maps

Details Bifurcations of homoclinic orbits in bimodal maps Bifurcations of homoclinic orbits in bimodal maps

1994-11-03

arxiv.org/abs/chao-dyn/9410010v2

Nonlinear Sciences

Chaotic Dynamics

11 pages, uuencoded compressed PostScript

Scientific paper

10.1103/PhysRevE.50.1653

We discuss the bifurcation structure of homoclinic orbits in bimodal one dimensional maps. The universal structure of these bifurcations with singular bifurcation points and the web of bifurcation lines through the parameter space are described. The bifurcations depend on two parameters (codimension 2 bifurcations). We find the bifurcation lines exactly in a symbolic dynamics parameter plane and numerically in the parameter planes of a polynomial map and a piecewise linear map.

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