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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
; | | Date: |
15 Apr 2002 | | Subject: | Chaotic Dynamics; Pattern Formation and Solitons | nlin.CD nlin.PS | | Abstract: | Basins generated by a noninvertible mapping formed by two symmetrically coupled logistic maps are studied when the only parameter lambda of 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. | | Source: | arXiv, nlin.CD/0204028 | | Services: | Forum | Review | PDF | Favorites | |
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