Adaptive Asymptotic Shape Synchronization of a Chaotic System with Applications for Image Encryption

Yangxin Luo, Yuanyuan Huang (), Fei Yu (), Diqing Liang and Hairong Lin
Additional contact information
Yangxin Luo: 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
Fei Yu: School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China
Diqing Liang: 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, 2024, vol. 13, issue 1, 1-18

Abstract: In contrast to previous research that has primarily focused on distance synchronization of states in chaotic systems, shape synchronization emphasizes the geometric shape of the attractors of two chaotic systems. Diverging from the existing work on shape synchronization, this paper introduces the application of adaptive control methods to achieve asymptotic shape synchronization for the first time. By designing an adaptive controller using the proposed adaptive rule, the response system under control is able to attain asymptotic synchronization with the drive system. This method is capable of achieving synchronization for models with parameters requiring estimation in both the drive and response systems. The control approach remains effective even in the presence of uncertainties in model parameters. The paper presents relevant theorems and proofs, and simulation results demonstrate the effectiveness of adaptive asymptotic shape synchronization. Due to the pseudo-random nature of chaotic systems and their extreme sensitivity to initial conditions, which make them suitable for information encryption, a novel channel-integrated image encryption scheme is proposed. This scheme leverages the shape synchronization method to generate pseudo-random sequences, which are then used for shuffling, scrambling, and diffusion processes. Simulation experiments demonstrate that the proposed encryption algorithm achieves exceptional performance in terms of correlation metrics and entropy, with a competitive value of 7.9971. Robustness is further validated through key space analysis, yielding a value of 10 210 × 2 512 , as well as visual tests, including center and edge cropping. The results confirm the effectiveness of adaptive asymptotic shape synchronization in the context of image encryption.

Keywords: adaptive control; shape synchronization; chaotic system; image encryption (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/1/128/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/1/128/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2024:i:1:p:128-:d:1557860

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().