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Chaotic Dynamics Analysis and FPGA Implementation Based on Gauss Legendre Integral

Author

Listed:
  • Li Wen

    (School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China)

  • Li Cui

    (School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China)

  • Hairong Lin

    (School of Electronic Information, Central South University, Changsha 410083, China)

  • Fei Yu

    (School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China)

Abstract

In this paper, we first design the corresponding integration algorithm and matlab program according to the Gauss–Legendre integration principle. Then, we select the Lorenz system, the Duffing system, the hidden attractor chaotic system and the Multi-wing hidden chaotic attractor system for chaotic dynamics analysis. We apply the Gauss–Legendre integral and the Runge–Kutta algorithm to the solution of dissipative chaotic systems for the first time and analyze and compare the differences between the two algorithms. Then, we propose for the first time a chaotic basin of the attraction estimation method based on the Gauss–Legendre integral and Lyapunov exponent and the decision criterion of this method. This method can better obtain the region of chaotic basin of attraction and can better distinguish the attractor and pseudo-attractor, which provides a new way for chaotic system analysis. Finally, we use FPGA technology to realize four corresponding chaotic systems based on the Gauss–Legendre integration algorithm.

Suggested Citation

  • Li Wen & Li Cui & Hairong Lin & Fei Yu, 2025. "Chaotic Dynamics Analysis and FPGA Implementation Based on Gauss Legendre Integral," Mathematics, MDPI, vol. 13(2), pages 1-23, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:201-:d:1563614
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