On \(q\)-deformed logistic maps. (English) Zbl 1496.37036
This paper is devoted to the study of \(q\)-deformations of the logistic family of maps with either a single or several \(q\)-deformations. The author first considers the stability of fixed points of these maps and characterizes when they are locally asymptotically stable and globally asymptotically stable. The complexity of \(q\)-deformations of maps in the logistic family is studied by computing their topological entropy. In the several \(q\)-deformations case, the author observes Parrondo’s paradox, according to which the composition of dynamically simple maps results in complex dynamical behavior. Parrondo’s paradox was also observed by J. Cánovas and M. Muñoz-Guillermo [Phys. Lett., A 383, No. 15, 1742–1754 (2019; Zbl 1476.62268)].
Reviewer: Steve Pederson (Atlanta)
MSC:
| 37E05 | Dynamical systems involving maps of the interval |
| 37C75 | Stability theory for smooth dynamical systems |
Citations:
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