Simulation of Recursive Functions by Means of Interval Analysis and Pseudo-Orbits

TL;DR

This paper presents a method that uses interval analysis and pseudo-orbits to simulate recursive functions, specifically applied to the logistic map, improving bounds on solutions.

Contribution

It introduces a novel approach combining pseudo-orbits and interval extensions to enhance simulation accuracy of recursive functions.

Findings

Reduced bounds of solutions using interval analysis

Effective simulation of logistic map with pseudo-orbits

Improved accuracy over traditional methods

Abstract

In this work we use intersection of different pseudo-orbits obtained by interval extensions to reduce the bounds of the exact solution provided by the toolbox Intlab. The method is applied on the logistic map.