Event-Triggered Impulsive Controller Design for Synchronization of Delayed Chaotic Neural Networks and Its Fractal Reconstruction: An Application to Image Encryption

•The effect of synchronisation on the master-slave NNs with time delay is examined.•The NN’s chaotic attractor is reconstructed using the fractal interpolation.•Reconstructed chaotic sequence is applied in image encryption.•Image encryption is carried out using RSA algorithm.•Various statistical mea...

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Published inApplied mathematical modelling Vol. 115; pp. 490 - 512
Main Authors Mohanrasu, S S, Udhayakumar, K, Priyanka, T M C, Gowrisankar, A, Banerjee, Santo, Rakkiyappan, R
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2023
Subjects
Chaotic neural networks
Fractal interpolation functions
Image encryption
Linear matrix inequalities
RSA public-key cryptosystems
Vertical scaling factors
Fractal interpolation functions
Image encryption
Linear matrix inequalities
RSA public-key cryptosystems
Chaotic neural networks
Vertical scaling factors
Online AccessGet full text
ISSN0307-904X
DOI10.1016/j.apm.2022.10.015

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Abstract •The effect of synchronisation on the master-slave NNs with time delay is examined.•The NN’s chaotic attractor is reconstructed using the fractal interpolation.•Reconstructed chaotic sequence is applied in image encryption.•Image encryption is carried out using RSA algorithm.•Various statistical measures are used to verify the efficacy. This paper examines synchronization of delayed chaotic neural networks with impulsive control, event-triggered impulsive control, and event-triggered delayed impulsive control. Lyapunov-based event-triggered mechanism is constructed to derive few sufficient conditions in terms of Linear Matrix Inequalities (LMIs). The feedback and event-triggered gain matrices are evaluated with the help of numerical packages. The fractal interpolation functions are employed to reconstruct the chaotic sequence of the neural networks since the chaotic attractor has self-similar properties and coincides with the fractal functions. In this study, a linear fractal interpolation is used to reconstruct both the master-slave chaotic attractor and the encrypted chaotic attractor, with optimized scaling factors. Finally, an application of the image encryption algorithm is given in terms of RSA public-key cryptosystems, permutation, and finite field diffusion for the chaotic sequence generated by fractal interpolation functions.
AbstractList •The effect of synchronisation on the master-slave NNs with time delay is examined.•The NN’s chaotic attractor is reconstructed using the fractal interpolation.•Reconstructed chaotic sequence is applied in image encryption.•Image encryption is carried out using RSA algorithm.•Various statistical measures are used to verify the efficacy. This paper examines synchronization of delayed chaotic neural networks with impulsive control, event-triggered impulsive control, and event-triggered delayed impulsive control. Lyapunov-based event-triggered mechanism is constructed to derive few sufficient conditions in terms of Linear Matrix Inequalities (LMIs). The feedback and event-triggered gain matrices are evaluated with the help of numerical packages. The fractal interpolation functions are employed to reconstruct the chaotic sequence of the neural networks since the chaotic attractor has self-similar properties and coincides with the fractal functions. In this study, a linear fractal interpolation is used to reconstruct both the master-slave chaotic attractor and the encrypted chaotic attractor, with optimized scaling factors. Finally, an application of the image encryption algorithm is given in terms of RSA public-key cryptosystems, permutation, and finite field diffusion for the chaotic sequence generated by fractal interpolation functions.
Author Banerjee, Santo
Priyanka, T M C
Rakkiyappan, R
Gowrisankar, A
Mohanrasu, S S
Udhayakumar, K
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  email: rakkigru@gmail.com
  organization: Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamil Nadu, India
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Keywords Fractal interpolation functions
Image encryption
Linear matrix inequalities
RSA public-key cryptosystems
Chaotic neural networks
Vertical scaling factors
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Snippet •The effect of synchronisation on the master-slave NNs with time delay is examined.•The NN’s chaotic attractor is reconstructed using the fractal...
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StartPage 490
SubjectTerms Chaotic neural networks
Fractal interpolation functions
Image encryption
Linear matrix inequalities
RSA public-key cryptosystems
Vertical scaling factors
Title Event-Triggered Impulsive Controller Design for Synchronization of Delayed Chaotic Neural Networks and Its Fractal Reconstruction: An Application to Image Encryption
URI https://dx.doi.org/10.1016/j.apm.2022.10.015
Volume 115
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