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

• Autor(a) principal: da Costa, Diogo Ricardo
• Data de Publicação: 2017
• Outros Autores: Medrano-T, Rene O. [UNIFESP], Leonel, Edson Denis
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNIFESP
• Texto Completo: http://dx.doi.org/10.1016/j.physa.2017.05.074; https://repositorio.unifesp.br/handle/11600/58173
• topic: Boundary crisis; Feigenbaum universality; Generalized logistic mapping

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.