A rigorous evaluation of the intermittence in the logistic map using lower bound error

TL;DR

This paper rigorously evaluates the duration of reliable intermittence observation in the logistic map using interval analysis and lower error bounds, highlighting the dependence on initial conditions.

Contribution

It introduces a method to determine the maximum simulation time for observing intermittence with numerical confidence in discrete maps.

Findings

Reliability of intermittency depends on initial conditions.

Interval analysis effectively estimates maximum observation time.

Four numerical examples demonstrate the method's efficiency.

Abstract

This article investigates the maximum time of simulation in which the phenomenon of the intermittence can be observed with numerical confidence in discrete maps. Interval analysis and the lower error limit were used. As a result, it was observed that the reliability of the intermittency is dependent on the initial condition. Four numerical examples show the efficiency of the proposal.