New results on finite-time projective synchronization for memristor-based hybrid delayed BAM neural networks with applications to DNA image encryption

Meng Li; Gulijiamali Maimaitiaili; Meng Li; Gulijiamali Maimaitiaili

doi:10.3934/math.2024481

AIMS Mathematics

2024, Volume 9, Issue 4: 9822-9846. doi: 10.3934/math.2024481

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New results on finite-time projective synchronization for memristor-based hybrid delayed BAM neural networks with applications to DNA image encryption

Meng Li ¹,
Gulijiamali Maimaitiaili ^{1,2
,
,}

1.
School of Mathematics Science, Xinjiang Normal University, Urumqi, Xinjiang 830017, China
2.
Xinjiang Key Laboratory of Mental Development and Learning Science, China

Received: 27 December 2023 Revised: 23 February 2024 Accepted: 28 February 2024 Published: 11 March 2024
MSC : 26E70, 34D06, 93E15

With the popularization of digital image technology, image information has inevitably developed to involved the disclosure of personal privacy; in this study, a color image encryption algorithm was designed to encrypt and decrypt images by using chaotic sequences of a class of memristor-based hybrid delayed bidirectional associative memory neural networks (MHDBAMNNs) to protect images from illegal acquisition and use. Additionally, the discontinuity problem of the right-hand side of the Filippov system due to the hopping property of the memristor has been treated by using differential inclusion and set-valued mapping theories, and a sufficient criterion for guaranteeing the synchronization of finite-time projections derived based on the drive-response concept, Lyppunov stability theorem, and inequality technique. To improve the security performance, a color image encryption algorithm based on a combination of Chen's hyperchaotic system and a DNA codec operation was adopted, also, the robustness and validity of our proposed approach was demonstrated through image performance analysis. Furthermore, the potential application of the model in secure transmission has been explored.
- memristor-based BAM network system,
- finite time projection synchronization,
- hybrid delays,
- DNA image encryption
Citation: Meng Li, Gulijiamali Maimaitiaili. New results on finite-time projective synchronization for memristor-based hybrid delayed BAM neural networks with applications to DNA image encryption[J]. AIMS Mathematics, 2024, 9(4): 9822-9846. doi: 10.3934/math.2024481

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Abstract

With the popularization of digital image technology, image information has inevitably developed to involved the disclosure of personal privacy; in this study, a color image encryption algorithm was designed to encrypt and decrypt images by using chaotic sequences of a class of memristor-based hybrid delayed bidirectional associative memory neural networks (MHDBAMNNs) to protect images from illegal acquisition and use. Additionally, the discontinuity problem of the right-hand side of the Filippov system due to the hopping property of the memristor has been treated by using differential inclusion and set-valued mapping theories, and a sufficient criterion for guaranteeing the synchronization of finite-time projections derived based on the drive-response concept, Lyppunov stability theorem, and inequality technique. To improve the security performance, a color image encryption algorithm based on a combination of Chen's hyperchaotic system and a DNA codec operation was adopted, also, the robustness and validity of our proposed approach was demonstrated through image performance analysis. Furthermore, the potential application of the model in secure transmission has been explored.

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