Construction and complexity analysis of new cubic chaotic maps based on spectral entropy algorithm

Abstract

This paper proposes two kind of new cubic chaotic maps based on Li-Yorke’s chaos criterion theorem, and gives the corresponding chaos discriminant conditions. The dynamical behaviors of systems are numerically simulated by nonlinear techniques including bifurcation diagrams and Laypunov exponents, and the simulation results show the cubic chaotic maps display chaotic characteristics as the provided theorems expect. Using spectral entropy algorithm, this paper analyses the complexity of chaotic sequences generated by cubic chaotic maps after quantitative process, and further compares the complexity of the chaotic pseudorandom sequences based on different quantitative methods. The results show different quantitative methods has a significant effect on the complexity of chaotic sequences; the pseudorandom sequences generated by the systems and quantitative method provided in this paper turns to have a better complexity. The above conclusions provide a theoretical basis for generating pseudorandom sequences with better quality.