On <i>q</i>-deformed logistic maps

Abstract

We consider the logistic family fa and a family of homeomorphisms φq. The q-deformed system is given by the composition map fa • φq. 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 fa • φq is dynamically complicated. We explore the dynamics when several q-deformations are applied.