A numerical study of universality and self-similarity in the Forced Logistic Map∗
نویسندگان
چکیده
We explore different two parametric families of quasi-periodically Forced Logistic Maps looking for universality and self-similarity properties. In the bifurcation diagram of the one-dimensional Logistic Map it is well known that there exist parameter values sn where the 2-periodic orbit is superattracting. Moreover, these parameter values lay between the parameters corresponding to two consecutive period doublings. In the quasi-periodically Forced Logistic Maps, these points are replaced by invariant curves, that undergo a (finite) sequence of period doublings. In this work we study numerically the presence of self-similarities in the bifurcation diagram of the invariant curves of these quasi-periodically Forced Logistic Maps. Our computations show a remarkable self-similarity for some of these families. We also show that this self-similarity cannot be extended to any quasi-periodic perturbation of the Logistic map.
منابع مشابه
A numerical Study of Universality and Self-Similarity in some Families of forced logistic Maps
We explore different two-parametric families of quasi-periodically Forced Logistic Maps looking for universality and self-similarity properties. In the bifurcation diagram of the one-dimensional Logistic Map, it is well known that there exist parameter values sn where the 2-periodic orbit is superattracting. Moreover, these parameter values lay between the parameters corresponding to two consec...
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