Revisiting the dynamic of Q-deformed logistic maps

TL;DR

This paper explores the complex dynamics of a $q$-deformed logistic map, revealing richer behaviors than previously studied deformations through stability analysis, entropy, and Lyapunov exponents.

Contribution

It introduces a new $q$-deformation of the logistic map and analyzes its stability and chaotic regions, demonstrating increased dynamical complexity.

Findings

Identification of stability regions for fixed points

Detection of complex dynamics via topological entropy

Observation of richer behavior compared to previous $q$-deformations

Abstract

We consider the logistic family and apply the $q$-deformation $\phi_q(x)=\frac{1-q^x}{1-q}$. We study the stability regions of the fixed points of the $q$-deformed logistic map and the regions where the dynamic is complex through topological entropy and Lyapunov exponents. Our results show that the dynamic of this deformed family is richer than that of the $q$-deformed family studied in [8].