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We explore different families of quasi-periodically Forced Logistic Maps forthe existence of universality and self-similarity properties. In thebifurcation diagram of the Logistic Map it is well known that there existparameter values $s_n$ where the $2^n$-periodic orbit is superattracting.Moreover these parameter values lay between one period doubling and the next.Under quasi-periodic forcing, the superattracting periodic orbits give birth totwo reducibility-loss bifurcations in the two dimensional parameter space ofthe Forced Logistic Map, both around the points $s_n$. In the present work westudy numerically the asymptotic behavior of the slopes of these bifurcationswith respect to $n$. This study evidences the existence of universalityproperties and self-similarity of the bifurcation diagram in the parameterspace.

Numerical evidences of universality and self-similarity in the Forced Logistic Map