On the Constructing Bifurcation Diagram of the Quadratic Map With Floating-Point Arithmetic

TL;DR

This paper investigates how floating-point arithmetic influences the construction of bifurcation diagrams for the quadratic map, revealing that initial condition restrictions significantly alter the map's behavior and bifurcation structure.

Contribution

It demonstrates the impact of floating-point arithmetic on bifurcation diagrams and highlights the importance of initial condition restrictions in such analyses.

Findings

Floating-point arithmetic causes significant differences in bifurcation diagrams.

Restrictions on initial conditions lead to notable changes in map behavior.

Results differ from traditional literature due to computational precision effects.

Abstract

This paper presents an analysis on the effects of floating-point arithmetic on the constructing bifurcation diagram of the quadratic map. More precisely, we are interested in showing the dependence of initial conditions to obtain some specific features of the diagram. With this study, it was possible to observe that when there is a restriction regarding the initial condition, the results present aspects with significant differences of the ones found in the literature regarding the behaviour of the map, consequently there is a considerable modification in its bifurcation diagram. We show that these difference are related to floating-point arithmetic