A New Simple Chaotic System with One Nonlinear Term

Yassine Bouteraa, Javad Mostafaee, Mourad Kchaou, Rabeh Abbassi, Houssem Jerbi and Saleh Mobayen ()
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Yassine Bouteraa: College of Computer Engineering and Sciences, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Javad Mostafaee: Multidisciplinary Center for Infrastructure Engineering, Shenyang University of Technology, Shenyang 110870, China
Mourad Kchaou: Department of Electrical Engineering, College of Engineering, University of Hail, Hail 55476, Saudi Arabia
Rabeh Abbassi: Department of Electrical Engineering, College of Engineering, University of Hail, Hail 55476, Saudi Arabia
Houssem Jerbi: Department of Industrial Engineering, College of Engineering, University of Hail, Hail 55476, Saudi Arabia
Saleh Mobayen: Graduate School of Intelligent Data Science, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 640301, Taiwan

Mathematics, 2022, vol. 10, issue 22, 1-17

Abstract: In this research article, a simple four-dimensional (4D) chaotic dynamic system with uncomplicated structure and only one nonlinear term is introduced. The features of the proposed design have been conducted with some standard nonlinear dynamic analysis and mathematical tools which show the chaotic nature. One of the most important indicators for detecting complexity of the chaotic systems is the Kaplan-York dimension of the system. Moreover, one of the main criteria of chaotic systems is its simplicity due to the reduction of operating costs. Therefore, it seems necessary to design a system as simple as possible and with high complexity. In this research, a comparison has been made between the proposed system and similar chaotic systems, which has given noticeable results. For the practical implementation of the proposed design, the circuit analysis using Multisim software has been employed. The proposed scheme has been used in the application of image encryption to show the efficiency of the proposed chaotic system and standard encryption tests have been performed. The rest of the numerical results have been conducted using MATLAB/Simulink software.

Keywords: chaotic system; equilibrium points; circuit design; attractor; image encryption/decryption (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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