Title: A new multistable jerk system with Hopf bifurcations, its electronic circuit simulation and an application to image encryption

Authors: Sundarapandian Vaidyanathan; Irene M. Moroz; Ahmed A. Abd El-Latif; Bassem Abd-El-Atty; Aceng Sambas

Addresses: Research and Development Centre, Vel Tech University, Chennai 600062, Tamil Nadu, India ' Mathematical Institute, University of Oxford, Oxford, England, UK ' Mathematics and Computer Science Department, Menoufia University, Shebin El-Kom, Al Minufya, Egypt ' Department of Computer Science, Faculty of Computers and Information, Luxor University, Luxor 85957, Egypt ' Department of Mechanical Engineering, Universitas Muhammadiyah Taskimalaya, Tasikmalaya, Jawa Barat 46196, Indonesia

Abstract: In this work, we announce a new 3-D jerk system and show that it is chaotic and dissipative with the calculation of the Lyapunov exponents of the system. By performing a detailed bifurcation analysis, we observe that the new jerk system exhibits Hopf bifurcations. It is also shown that the new jerk system exhibits multistability behaviour with two coexisting chaotic attractors. An electronic circuit simulation of the jerk system is built using Multisim. Finally, we design a new approach to image encryption as a cryptographic application of our chaotic jerk system. The simulation outcomes prove the efficiency of the proposed encryption scheme with high security.

Keywords: bifurcations; chaos; chaotic systems; Hopf bifurcations; multi-stability; attractors; circuit design; jerk systems; image encryption; cryptography.

DOI: 10.1504/IJCAT.2021.10044864

International Journal of Computer Applications in Technology, 2021 Vol.67 No.1, pp.29 - 46

Received: 25 Sep 2020
Accepted: 05 Dec 2020

Published online: 07 Feb 2022 *

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