The fractional difference form of sine chaotification model

Abstract To improve the chaos complexity of existing chaotic maps, the fractional difference form of sine chaotification model (FSCM) is proposed in this paper based on discrete fractional calculus. In order to show its effect, we apply it to three chaotic maps. And the bifurcation diagrams and Lyapunov exponent of the generated new map are studied numerically. The experimental results show that FSCM has more stable and efficient performance. In addition, the dynamic behavior of the generated new map varies with the fractional order, which can be observed through analysis. Finally, FSCM is used for image encryption to show its performance in practical applications. The analysis of the results shows that the chaotic behavior of the fractional map generated by FSCM is more complex and its encryption effect is better.