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A New Simple Chaotic System with One Nonlinear Term

Author

Listed:
  • Yassine Bouteraa

    (College of Computer Engineering and Sciences, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Control and Energy Management Laboratory (CEM Lab.), Ecole Nationale d’Ingenieurs de Sfax (ENIS), Institut Superieur de Biotechnologie de Sfax (ISBS), University of Sfax, Sfax 3038, Tunisia)

  • 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)

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.

Suggested Citation

  • Yassine Bouteraa & Javad Mostafaee & Mourad Kchaou & Rabeh Abbassi & Houssem Jerbi & Saleh Mobayen, 2022. "A New Simple Chaotic System with One Nonlinear Term," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4374-:d:978691
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    References listed on IDEAS

    as
    1. Lai, Qiang & Nestor, Tsafack & Kengne, Jacques & Zhao, Xiao-Wen, 2018. "Coexisting attractors and circuit implementation of a new 4D chaotic system with two equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 92-102.
    2. Gong, Li-Hua & Luo, Hui-Xin & Wu, Rou-Qing & Zhou, Nan-Run, 2022. "New 4D chaotic system with hidden attractors and self-excited attractors and its application in image encryption based on RNG," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    3. Muhammad Marwan & Vagner Dos Santos & Muhammad Zainul Abidin & Anda Xiong, 2022. "Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems," Mathematics, MDPI, vol. 10(11), pages 1-15, June.
    4. Omar Guillén-Fernández & Esteban Tlelo-Cuautle & Luis Gerardo de la Fraga & Yuma Sandoval-Ibarra & Jose-Cruz Nuñez-Perez, 2022. "An Image Encryption Scheme Synchronizing Optimized Chaotic Systems Implemented on Raspberry Pis," Mathematics, MDPI, vol. 10(11), pages 1-23, June.
    5. Mobayen, Saleh & Alattas, Khalid A. & Fekih, Afef & El-Sousy, Fayez F.M. & Bakouri, Mohsen, 2022. "Barrier function-based adaptive nonsingular sliding mode control of disturbed nonlinear systems: A linear matrix inequality approach," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    6. Jiri Petrzela, 2022. "Chaotic and Hyperchaotic Dynamics of a Clapp Oscillator," Mathematics, MDPI, vol. 10(11), pages 1-20, May.
    7. Castañeda, Carlos E. & López-Mancilla, D. & Chiu, R. & Villafaña-Rauda, E. & Orozco-López, Onofre & Casillas-Rodríguez, F. & Sevilla-Escoboza, R., 2019. "Discrete-time neural synchronization between an Arduino microcontroller and a Compact Development System using multiscroll chaotic signals," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 269-275.
    8. Khalid A. Alattas & Javad Mostafaee & Aceng Sambas & Abdullah K. Alanazi & Saleh Mobayen & Mai The Vu & Anton Zhilenkov, 2021. "Nonsingular Integral-Type Dynamic Finite-Time Synchronization for Hyper-Chaotic Systems," Mathematics, MDPI, vol. 10(1), pages 1-21, December.
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