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Complex patterns on the plane: different types of basin fractalization in a two-dimensional mapping

Ricardo Lopez-Ruiz·Daniele Fournier-Prunaret
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Abstract

Basins generated by a noninvertible mapping formed by two symmetrically coupled logistic maps are studied when the only parameter λof the system is modified. Complex patterns on the plane are visualised as a consequence of basins' bifurcations. According to the already established nomenclature in the literature, we present the relevant phenomenology organised in different scenarios: fractal islands disaggregation, finite disaggregation, infinitely disconnected basin, infinitely many converging sequences of lakes, countable self-similar disaggregation and sharp fractal boundary. By use of critical curves, we determine the influence of zones with different number of first rank preimages in the mechanisms of basin fractalization.

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Ricardo Lopez-Ruiz, Daniele Fournier-Prunaret. 2002-04-15. Complex patterns on the plane: different types of basin fractalization in a two-dimensional mapping. https://doi.org/10.1142/s0218127403006558

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