Statistical analysis of chaotic stochastic properties based on the logistic map and Fibonacci sequence

The chaotic cryptosystems are widely researched in the scientific and technical fields. But the dynamical degradation is a hindrance to digital chaotic maps. In this paper, we present a detailed statistical analysis of the mixed chaotic series based on the logistic map and Fibonacci sequence, which convert the value of the logistic map into the integer number by Fibonacci sequence. The experimental results show that the mixed chaotic series have the desired dynamics and randomness with the range of (0, 256). It is the prevention and remedy to the dynamical degradation of chaotic maps. It can be applied to the chaotic cryptosystems and security communications.