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Volume 14
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Dynamic Analysis and Application of 6D Multistable Memristive Chaotic System with Wide Range of Hyperchaotic States

by
Fei Yu
1,
Yumba Musoya Gracia
2,
Rongyao Guo
1,
Zhijie Ying
1,
Jiarong Xu
1,
Wei Yao
1,
Jie Jin
3,* and
Hairong Lin
4
1
School of Physics and Electronic Science, Changsha University of Science and Technology, Changsha 410114, China
2
School of Computer Science and Technology, Changsha University of Science and Technology, Changsha 410076, China
3
School of Information Engineering, Changsha Medical University, Changsha 410219, China
4
School of Electronic Information, Central South University, Changsha 410083, China
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(8), 638; https://doi.org/10.3390/axioms14080638
Submission received: 10 July 2025 / Revised: 11 August 2025 / Accepted: 14 August 2025 / Published: 15 August 2025
(This article belongs to the Special Issue Nonlinear Dynamical System and Its Applications)
Versions Notes

Abstract

In this study, we present a novel, six-dimensional, multistable, memristive, hyperchaotic system model demonstrating two positive Lyapunov exponents. With the maximum Lyapunov exponents surpassing 21, the developed system shows pronounced hyperchaotic behavior. The dynamical behavior was analyzed through phase portraits, bifurcation diagrams, and Lyapunov exponent spectra. Parameter b was a key factor in regulating the dynamical behavior of the system, mainly affecting the strength and direction of the influence of z1 on z2. It was found that when the system parameter b was within a wide range of [13,300], the system remained hyperchaotic throughout. Analytical establishment of multistability mechanisms was achieved through invariance analysis of the state variables under specific coordinate transformations. Furthermore, offset boosting control was realized by strategically modulating the fifth state variable, z5. The FPGA-based experimental results demonstrated that attractors observed via an oscilloscope were in close agreement with numerical simulations. To validate the system’s reliability for cybersecurity applications, we designed a novel image encryption method utilizing this hyperchaotic model. The information entropy of the proposed encryption algorithm was closer to the theoretical maximum value of 8. This indicated that the system can effectively disrupt statistical patterns. Experimental outcomes confirmed that the proposed image encryption method based on the hyperchaotic system exhibits both efficiency and reliability.
Keywords: multistable memristive hyperchaotic system (MMHS); Lyapunov exponents; bifurcation; wide range; multistability; offset boosting control; FPGA; image encryption multistable memristive hyperchaotic system (MMHS); Lyapunov exponents; bifurcation; wide range; multistability; offset boosting control; FPGA; image encryption

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MDPI and ACS Style

Yu, F.; Gracia, Y.M.; Guo, R.; Ying, Z.; Xu, J.; Yao, W.; Jin, J.; Lin, H. Dynamic Analysis and Application of 6D Multistable Memristive Chaotic System with Wide Range of Hyperchaotic States. Axioms 2025, 14, 638. https://doi.org/10.3390/axioms14080638

AMA Style

Yu F, Gracia YM, Guo R, Ying Z, Xu J, Yao W, Jin J, Lin H. Dynamic Analysis and Application of 6D Multistable Memristive Chaotic System with Wide Range of Hyperchaotic States. Axioms. 2025; 14(8):638. https://doi.org/10.3390/axioms14080638

Chicago/Turabian Style

Yu, Fei, Yumba Musoya Gracia, Rongyao Guo, Zhijie Ying, Jiarong Xu, Wei Yao, Jie Jin, and Hairong Lin. 2025. "Dynamic Analysis and Application of 6D Multistable Memristive Chaotic System with Wide Range of Hyperchaotic States" Axioms 14, no. 8: 638. https://doi.org/10.3390/axioms14080638

APA Style

Yu, F., Gracia, Y. M., Guo, R., Ying, Z., Xu, J., Yao, W., Jin, J., & Lin, H. (2025). Dynamic Analysis and Application of 6D Multistable Memristive Chaotic System with Wide Range of Hyperchaotic States. Axioms, 14(8), 638. https://doi.org/10.3390/axioms14080638

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