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Dynamic behavior of fractional-order memristive time-delay system and image encryption application

School of Electronics and Information Engineering, Anhui University, Hefei 230601, China

National Engineering Research Center, for Agro-Ecological Big Data Analysis and Application, Anhui University, Hefei 230601, China

E-mail Address: dliang@ahu.edu.cn

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Dawei Ding

School of Electronics and Information Engineering, Anhui University, Hefei 230601, China

National Engineering Research Center, for Agro-Ecological Big Data Analysis and Application, Anhui University, Hefei 230601, China

E-mail Address: dwding@ahu.edu.cn

Corresponding author.

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, and

Yongbing Hu

School of Electronics and Information Engineering, Anhui University, Hefei 230601, China

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https://doi.org/10.1142/S0217984921502717Cited by:6 (Source: Crossref)

Abstract

This paper presents dynamic behavior of a fractional-order memristive time-delay system and its application in image encryption. First, a fractional-order memristive time-delay system is proposed, and the stability and bifurcation behaviors of the system are theoretically analyzed. Some limited conditions for describing the stability interval and switching between different dynamic behaviors are derived. Second, the dynamic characteristics of the system are analyzed through the coexisting attractors, coexisting bifurcation diagrams, the Largest Lyapunov exponents (LLE), the 0-1 test. When parameters change, such as time delay and fractional order, the system transits from steady state to periodic state, single scroll chaotic state, double scroll chaotic state. Furthermore, an image encryption scheme based on the fractional-order memristive time-delay system is introduced, and some statistical features are analyzed. Finally, numerical simulations verify the validity of the theoretical analysis and safety of the image encryption scheme based on the fractional-order delayed memristive chaotic system.

Keywords:

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