ON q-DEFORMED LOGISTIC MAPS

We consider the logistic family fa and a family of homeomorphisms phi(q). The q-deformed system is given by the composition map f(a) circle phi(q). We study when this system has non zero fixed points which are LAS and GAS. We also give an alternative approach to study the dynamics of the q-deformed system with special emphasis on the so-called Parrondo's paradox finding parameter values a for which fa is simple while f(a) circle phi(q) is dynamically complicated. We explore the dynamics when several q-deformations are applied.

Automated summary

The paper discusses the non-zero fixed points of the composition map f(a) circle phi(q) of the logistic family fa and a family of homeomorphisms phi(q), as well as the dynamics of the q-deformed system with special emphasis on parameters values that exhibit Parrondo's paradox. The study explores the dynamics when multiple q-deformations are applied.