Fractional-order double-ring erbium-doped fiber laser chaotic system and its application on image encryption

Laser chaotic systems have been extensively studied and applied in the past 20 years. However, the fractional form of the chaotic system of erbium-doped fiber laser has not been studied yet. Therefore, this paper proposes a fractional-order double-ring erbium-doped fiber laser chaotic system. The dynamic characteristics of the system are studied by phase diagram, bifurcation diagram, Lyapunov exponent spectrum, Spectral Entropy (SE) complexity, and coexisting attractors. At the same time, the digital circuit of the new system is implemented on the digital signal processing (DSP) platform. Compared with integer-order double-ring erbium-doped fiber laser chaotic systems, this fractional-order chaotic system has more complex dynamics and higher sensitivity and randomness. Finally, the fractional-order double-ring erbium-doped fiber laser chaotic system is applied to the image encryption algorithm with the improved gravitation model. In this encryption algorithm, the diffusion part uses an improved universal gravitation model, and the Zigzag algorithm scrambles the pixels. The security of the algorithm is analyzed. The analyses of the experimental results show that the image encryption scheme proposed in this paper has a good encryption effect and good security performance. The research in this paper provides theoretical guidance and experimental basis for the research of fractional-order laser chaotic secure communication.