Route to chaos and some properties in the boundary crisis of a generalized logistic mapping

Route to chaos and some properties in the boundary crisis of a generalized logistic mapping

Author da Costa, Diogo Ricardo Google Scholar
Medrano-T, Rene O. Autor UNIFESP Google Scholar
Leonel, Edson Denis Google Scholar
Abstract A generalization of the logistic map is considered, showing two control parameters a and,8 that can reproduce different logistic mappings, including the traditional second degree logistic map, cubic, quartic and all other degrees. We introduce a parametric perturbation such that the original logistic map control parameter R changes its value periodically according an additional parameter omega = 2/q. The value of q gives this period. For this system, an analytical expression is obtained for the first bifurcation that starts a period-doubling cascade and, using the Feigenbaum Universality, we found numerically the accumulation point R-c where the cascade finishes giving place to chaos. In the second part of the paper we study the death of this chaotic behavior due to a boundary crisis. At the boundary crisis, orbits can reach a maximum value X = X-max, = 1. When it occurs, the trajectory is mapped to a fixed point at X = 0. We show that there exist a general recursive formula for initial conditions that lead to X = X-max. 2017 Elsevier B.V. All rights reserved.
Keywords Boundary crisis
Feigenbaum universality
Generalized logistic mapping
xmlui.dri2xhtml.METS-1.0.item-coverage Amsterdam
Language English
Sponsor Center for Scientific Computing (NCC/GridUNESP) of the Sao Paulo State University (UNESP)
Date 2017
Published in Physica A-Statistical Mechanics And Its Applications. Amsterdam, v. 486, p. 674-680, 2017.
ISSN 0378-4371 (Sherpa/Romeo, impact factor)
Publisher Elsevier Science Bv
Extent 674-680
Origin http://dx.doi.org/10.1016/j.physa.2017.05.074
Access rights Open access Open Access
Type Article
Web of Science ID WOS:000406988000056
URI https://repositorio.unifesp.br/handle/11600/58173

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