A q-deformed logistic map and its implications

TL;DR

This paper introduces a q-deformed logistic map with unique concavity and variable stability, exploring its chaotic and regular regimes and implications for Parrondo's paradox.

Contribution

It proposes a novel q-deformed logistic map and analyzes its stability, bifurcations, and implications, extending understanding of nonlinear dynamical systems.

Findings

The q-deformed logistic map exhibits concavity in parts of the x-space.

It has distinct one-cycle and two-cycle fixed points from the standard logistic map.

Changing the deformation parameter q transitions the system between chaos and order.

Abstract

A new q-deformed logistic map is proposed and it is found to have concavity in parts of the x-space. Its one-cycle and two-cycle non-trivial fixed points are obtained which are found to be qualitatively and quantitatively different from those of the usual logistic map. The stability of the proposed q-logistic map is studied using Lyapunov exponent and with a change in the value of the deformation parameter q, one is able to go from the chaotic to regular dynamical regime. The implications of this q-logistic map on Parrondo's paradox are examined.