Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encrypt
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ORIGINAL ARTICLE
Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption Zeric Tabekoueng Njitacke1,2
•
Sami Doubla Isaac2,3 • Tsafack Nestor2,3 • Jacques Kengne2
Received: 19 June 2020 / Accepted: 14 October 2020 Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract In this contribution, the problem of multistability control in a simple model of 3D HNNs as well as its application to biomedical image encryption is addressed. The space magnetization is justified by the coexistence of up to six disconnected attractors including both chaotic and periodic. The linear augmentation method is successfully applied to control the multistable HNNs into a monostable network. The control of the coexisting four attractors including a pair of chaotic attractors and a pair of periodic attractors is made through three crises that enable the chaotic attractors to be metamorphosed in a monostable periodic attractor. Also, the control of six coexisting attractors (with two pairs of chaotic attractors and a pair of periodic one) is made through five crises enabling all the chaotic attractors to be metamorphosed in a monostable periodic attractor. Note that this controlled HNN is obtained for higher values of the coupling strength. These interesting results are obtained using nonlinear analysis tools such as the phase portraits, bifurcations diagrams, graph of maximum Lyapunov exponent, and basins of attraction. The obtained results have been perfectly supported using the PSPICE simulation environment. Finally, a simple encryption scheme is designed jointly using the sequences of the proposed HNNs and the sequences of real/imaginary values of the Julia fractals set. The obtained cryptosystem is validated using some well-known metrics. The proposed method achieved entropy of 7.9992, NPCR of 99.6299, and encryption time of 0.21 for the 256*256 sample 1 image. Keywords Hopfield neural networks (HNNs) Space magnetization Multistability control PSPICE simulations Biomedical images encryption
1 Introduction Hopfield neural network (HNN) was introduced for the first time by Hopfield in 1984 [1]. From then, a better understanding of the dynamical behavior of the Hopfield neural & Zeric Tabekoueng Njitacke [email protected] 1
Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon
2
Unite´ de Recherche D’Automatique et Informatique Applique´e (URAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang, Cameroon
3
Unite´ de Recherche de Matie`re Condense´e, d’Electronique et de Traitement du Signal (URAMACETS), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon
network (HNN) is of major importance in the study of information processing and engineering applications [2, 3], such as pattern recognition [2], associative memory, and signal processing [3]. In addi
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