Chaos in fractional-order discrete neural networks with application to image encryption
Abstract
In this paper, a three-dimensional fractional-order (FO) discrete Hopfield neural network (FODHNN) in the left Caputo discrete delta's sense is proposed, the dynamic behavior and synchronization of FODHNN are studied, and the system is applied to image encryption. First, FODHNN is shown to exhibit rich nonlinear dynamics behaviors. Phase portraits, bifurcation diagrams and Lyapunov exponents are carried out to verify chaotic dynamics in this system. Moreover, by using stability theorem of FO discrete linear systems, a suitable control scheme is designed to achieve synchronization of the FODHNN. Finally, image encryption system based on the chaotic FODHNN is presented. Some security analysis and tests are given to show the effective of the encryption system.
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Liping Chen and Hao Yin [128,129] constructed a 3D fractional-order discrete Hopfield neural network (FODHNN) with chaotic dynamics features.
“Liping Chen and Hao Yin [128,129] constructed a 3D fractional-order (FO) discrete Hopfield neural network (FODHNN), which has chaotic dynamics features, in the left Caputo discrete delta's sense.”
From Chaos-Based Image Encryption: Review, Application, and Challenges (2023) · cites this paper as [128]
Cites
A color image cryptosystem based on dynamic DNA encryption and chaos
Chai, X., Fu, X., Gan, Z., Lu, Y., & Chen, Y. (2019) · Signal Processing · doi:10.1016/j.sigpro.2018.09.029 · Cited by 573 · see citing works
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Chaos-Based Image Encryption: Review, Application, and Challenges
Zhang, B., & Liu, L. (2023) · Mathematics · doi:10.3390/math11112585 · Cited by 328 · see citing works
“Liping Chen and Hao Yin [128,129] constructed a 3D fractional-order (FO) discrete Hopfield neural network (FODHNN), which has chaotic dynamics features, in the left Caputo discrete delta’s sense.”
BackgroundMeng, F.-Q., & Wu, G. (2024) · Expert Systems with Applications · doi:10.1016/j.eswa.2024.124413 · Cited by 144 · see citing works
- Authors
- Chen, L., Yin, H., Huang, T., Yuan, L., Zheng, S., & Yin, L.
- Affiliations
- Hefei University of Technology (CN)
- Texas A&M University at Qatar (QA)
- South China Agricultural University (CN)
- Zhejiang University of Finance and Economics (CN)
- Corresponding author
- Zheng, Song
- Venue
- Neural Networks
- Publisher
- Elsevier BV
- Published
- 2020-05
- Volume
- 125
- Pages
- 174-184
- ISSN
- 0893-6080 (ISSN-L)
- OpenAlex
- W3007442310
- Cited by
- 255
- References
- 1
- Citations by year
- 2026: 11 · 2025: 33 · 2024: 40 · 2023: 52 · 2022: 57 · 2021: 44 · 2020: 18
- FWCI
- 16.62
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Neural Networks (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Natural Science Funds of China (61403115, 11571016, 11971032)
- Ministry of Education of China (19YJCZH265)
- Fundamental Research Funds for the Central Universities, China (JZ2016HGXJ0022)
- Science and Technology Program of Guangzhou, China (201707010031)
- First Class Discipline of Zhejiang-
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
- Physical Sciences › Computer Science › Computer Networks and Communications › Neural Networks Stability and Synchronization
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Keywords
- Hopfield neural network, chaos, image encryption, synchronization, nonlinear dynamics, bifurcation, Lyapunov exponents, chaos control, encryption security
- MeSH terms
- Algorithms, Humans, Pattern Recognition, Automated, Computer Security, Neural Networks, Computer, Nonlinear Dynamics
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