Eur. Phys. J. Plus (2022) 137: 682
https://doi.org/10.1140/epjp/s13360-022-02811-7

Regular Article

Multistability analysis and color image encryption application of a fractional-order hyperchaotic system with double coupled memristors

¹ School of Electronics and Information Engineering, Anhui University, 230601, Hefei, China
² Ecological Big Data Analysis and Application, National Engineering Research Center for Agro, Anhui University, 230601, Hefei, China
³ China Academy of Information and Communications Technology (CAICT), Haidian District, No. 52 Huayuan North Road, Beijing, China

^e hwzhang@ahu.edu.cn

Received: 23 March 2022
Accepted: 6 May 2022
Published online: 10 June 2022

Abstract

In this paper, a novel fractional-order hyperchaotic system with double coupled memristors is proposed, and the hyperchaotic sequences generated by our system are applied to color image encryption. Firstly, the fractional-order mathematical model of the double coupled memristor is designed, which displays some different characteristics. Secondly, the stability of the fractional-order hyperchaotic system on the double coupled memristors is analyzed. Thirdly, complex dynamical behaviors of the novel system are analyzed using bifurcation diagram, Lyapunov diagram, phase diagram and attraction basin, and multistability phenomena are observed when the initial values are changed; therefore, the system can be applied to information security field. Finally, a color image encryption scheme on DNA coding is proposed, and the security of the scheme is evaluated by different attack methods. Numerical simulation indicates the validity of the theoretical analysis and robustness of the proposed image encryption scheme.