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Development of a Family of Chaotic Systems with Infinite Equilibria and Its Application for Image Encryption

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  • Xiaofeng Li
  • Yulong Bai
  • Weishuan Pan
  • Di Wang
  • Yong-Jie Ma

Abstract

Fourth‐order autonomous nonlinear differential equations can exhibit chaotic properties. In this study, we propose a family of fourth‐order chaotic systems with infinite equilibrium points whose equilibria form closed curves of different shapes. First, the phase diagrams and Lyapunov exponents (LEs) of the system family are simulated. The results show that the system family has complex phase diagrams and dynamic behaviors. Simulation analysis of the Poincarè mapping and bifurcation diagrams shows that the system has chaotic characteristics. The circuit simulation model is constructed and simulated in Multisim. The circuit simulation results coincide with the numerical simulation results, which verifies the circuit feasibility of the system. Then, based on Lyapunov stability theory and the adaptive control method, the synchronous control of the system with infinite equilibria is designed. Numerical simulation results verify that the system synchronization with the adaptive control method is well. Finally, the synchronous drive system is used for image encryption, the response system is used for decryption, and color image encryption is realized by combining deoxyribonucleic acid (DNA) coding and operating rules. Therefore, this study not only enriched the research on infinite equilibria chaotic systems but also further expanded secure communication technology by combining chaotic synchronization control and DNA coding in image encryption.

Suggested Citation

  • Xiaofeng Li & Yulong Bai & Weishuan Pan & Di Wang & Yong-Jie Ma, 2022. "Development of a Family of Chaotic Systems with Infinite Equilibria and Its Application for Image Encryption," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:1250489
    DOI: 10.1155/2022/1250489
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    References listed on IDEAS

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    1. Xiong Wang & Viet-Thanh Pham & Christos Volos, 2017. "Dynamics, Circuit Design, and Synchronization of a New Chaotic System with Closed Curve Equilibrium," Complexity, Hindawi, vol. 2017, pages 1-9, February.
    2. Reza Rahmani & Saleh Mobayen & Afef Fekih & Jong-Suk Ro, 2021. "Robust Passivity Cascade Technique-Based Control Using RBFN Approximators for the Stabilization of a Cart Inverted Pendulum," Mathematics, MDPI, vol. 9(11), pages 1-11, May.
    3. Hamede Karami & Saleh Mobayen & Marzieh Lashkari & Farhad Bayat & Arthur Chang, 2021. "LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation," Mathematics, MDPI, vol. 9(10), pages 1-15, May.
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