Route to chaos and some properties in the boundary crisis of a generalized logistic mapping
Data
2017
Autores
Medrano-T, Rene O. 
Tipo
Artigo
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Resumo
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.
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Citação
Physica A-Statistical Mechanics And Its Applications. Amsterdam, v. 486, p. 674-680, 2017.