Weak insensitivity to initial conditions at the edge of chaos in the logistic map

TL;DR

This paper explores the behavior of the logistic map at the edge of chaos, demonstrating that Tsallis entropy effectively characterizes the system's approach to attractors even at weak insensitivity points.

Contribution

It extends the application of Tsallis non-extensive thermodynamics to include weakly insensitive points at the edge of chaos in the logistic map.

Findings

Tsallis entropy describes the approach to attractors at the edge of chaos.

Generalized entropy with appropriate q value captures weak insensitivity.

Analysis of tangent points confirms the entropy's effectiveness.

Abstract

We extend existing studies of weakly sensitive points within the framework of Tsallis non-extensive thermodynamics to include weakly insensitive points at the edge of chaos. Analyzing tangent points of the logistic map we have verified that the generalized entropy with suitable entropic index q correctly describes the approach to the attractor.