A Wide-Range Adjustable Conservative Memristive Hyperchaotic System with Transient Quasi-Periodic Characteristics and Encryption Application

Fei Yu (), Bohong Tan, Ting He, Shaoqi He, Yuanyuan Huang, Shuo Cai and Hairong Lin
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Fei Yu: School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China
Bohong Tan: School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China
Ting He: School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China
Shaoqi He: School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China
Yuanyuan Huang: School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China
Shuo Cai: School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China
Hairong Lin: School of Electronic Information, Central South University, Changsha 410083, China

Mathematics, 2025, vol. 13, issue 5, 1-23

Abstract: In comparison with dissipative chaos, conservative chaos is better equipped to handle the risks associated with the reconstruction of phase space due to the absence of attractors. This paper proposes a novel five-dimensional (5D) conservative memristive hyperchaotic system (CMHS), by incorporating memristors into a four-dimensional (4D) conservative chaotic system (CCS). We conducted a comprehensive analysis, using Lyapunov exponent diagrams, bifurcation diagrams, phase portraits, equilibrium points, and spectral entropy maps to thoroughly verify the system’s chaotic and conservative properties. The system exhibited characteristics such as hyperchaos and multi-stability over an ultra-wide range of parameters and initial values, accompanied by transient quasi-periodic phenomena. Subsequently, the pseudorandom sequences generated by the new system were tested and demonstrated excellent performance, passing all the tests set by the National Institute of Standards and Technology (NIST). In the final stage of the research, an image-encryption application based on the 5D CMHS was proposed. Through security analysis, the feasibility and security of the image-encryption algorithm were confirmed.

Keywords: conservative hyperchaotic system; memristor; wide range; transient quasi-period; image encryption (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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