Dynamic analysis of fractional-order memristive chaotic system with time delay and its application in color image encryption based on DNA encoding

This paper proposes a fractional-order delayed memristive chaotic system and studies its dynamic analysis, and then a color image is encrypted based on the chaotic system and DNA encoding. First, the stability and bifurcation behaviors of the fractional-order memristive chaotic system with time delay are investigated and some sufficient conditions of the stability are obtained. Second, the Largest Lyapunov exponent, bifurcation diagram and K of the 0–1 test of the novel system are calculated, and they are shown by coexisting bifurcation, coexisting attractors, coexisting plot of p-q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p-q$$\end{document} and so on. All of these indicate that the novel system exists the abundant dynamic characteristics. Finally, a color image encryption scheme based on the proposed system is introduced, and the security is evaluated by statistical analysis and different attacks. Numerical simulation proves the validity of the theoretical analysis and high security of the proposed image encryption scheme.