A Chaotification model based on sine and cosecant functions for enhancing chaos

Abstract

Chaotic maps with higher chaotic complexity are urgently needed in many application scenarios. This paper proposes a chaotification model based on sine and cosecant functions (CMSC) to improve the dynamic properties of existing chaotic maps. CMSC can generate a new map with higher chaotic complexity by using the existing one-dimensional (1D) chaotic map as a seed map. To discuss the performance of CMSC, the chaos properties of CMSC are analyzed based on the mathematical definition of the Lyapunov exponent (LE). Then, three new maps are generated by applying three classical 1D chaotic maps to CMSC respectively, and the dynamic behaviors of the new maps are analyzed in terms of fixed point, bifurcation diagram, sample entropy (SE), etc. The results of the analysis demonstrate that the new maps have a larger chaotic region and excellent chaotic characteristics.