Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption

Zeric Tabekoueng Njitacke; Sami Doubla Isaac; Tsafack Nestor; Jacques Kengne

doi:10.1007/s00521-020-05451-z

Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption

Neural Comput Appl. 2021;33(12):6733-6752. doi: 10.1007/s00521-020-05451-z. Epub 2020 Nov 5.

Authors

Zeric Tabekoueng Njitacke^{1

2}, Sami Doubla Isaac^{2

3}, Tsafack Nestor^{2

3}, Jacques Kengne²

Affiliations

¹ Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon.
² Unité de Recherche D'Automatique et Informatique Appliquée (URAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang, Cameroon.
³ Unité de Recherche de Matière Condensée, d'Electronique et de Traitement du Signal (URAMACETS), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon.

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: Biomedical images encryption; Hopfield neural networks (HNNs); Multistability control; PSPICE simulations; Space magnetization.