Abstract
In this paper, a one parameter family (Fβ)β∈(0,1) of maps of the unit square I×I is studied. We observe that, for some values of parameter, our model exhibits one chaotic attractor Aβ,0, lying in the invariant subspace I×{0}, with a locally riddled basin of attraction. Rigorous analysis for the occurrence of locally riddled basin is given. Using the monotonicity and concavity of the fiber maps in our model, we give a classification, with respect to the number of attracting invariant graphs. We examine the bifurcation effects that appear in our model on varying parameter; in particular, a nonregular temporal bursting and the appearance of an on-off intermittency is investigated. Finally, we show that the model undergoes a nonhysteretic blowout bifurcation.
Published Version
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