Reliability analysis of the Logistic Map's pseudo-orbits through the Delta-Epsilon limit definition

Samuel Júlio dos Santos Silva¹; Vinicius da Silva Borges¹; Gabriel Hugo ́Alvares Silva¹; Erivelton Geraldo Nepomuceno¹

¹ Universidade Federal de São João Del Rei

Resumo

This paper reports the use of Delta-Epsilon limit definition as a way of evaluating a maximum number of iterations for the simulation of Logistic Map. This was possible by showing that logistic map is continuous and the error propagation is related to the nth composed function. It has been shown an error relationship with the number of iterations. Thus, the proposed method seeks to relate an arbitrary precision value to the number of iterations. With an analysis of the results, it is clear that for a result with a certain degree of precision one must be consider the number of iterations.

Palavras-chave: Logistic Map; IEEE 754; Nonlinear Dynamic Systems; Chaos; Delta-Epsilon; Limit Definition