Period Analysis of Chaotic Systems under Finite Precisions

Abstract

Theoretically, chaotic systems or chaotic maps have ideal complex dynamics. However, due to the finite precisions of the simulation software and digital devices, dynamic degradation and short period phenomenon will occur which is known as the finite precision effect. Thus, the short period phenomenon severely affects the performances of chaotic system in its application of secure communication and multimedia encryption etc. In this paper, the hash table is used to fast position the period of chaotic sequence, then calculate and analyze the relationships between computational precision and period length of digital chaotic systems. The experimental results show that the finite precision has a great influence on the periods of chaotic systems. The proposed method provides a quantitative analysis for the finite precision effect of the chaotic systems, which can aid designing the mechanisms to counteract the dynamic degradations and enhance the security performance.