A MBPAF-memristive Hopfield neural network and its application in image encryption.

Area of Science:

• Computational neuroscience
• Chaos theory
• Cryptography

Background:

• Nonlinear activation functions are crucial for neural network complexity.
• Memristive Hopfield Neural Networks (MHNNs) offer potential for complex dynamics.
• Existing activation functions may limit the hyper-chaotic behavior generation in MHNNs.

Purpose of the Study:

• To design a novel mixed-bipower activation function (MBPAF) with adjustable parameters.
• To propose a new MBPAF-Memristive Hopfield Neural Network (MBPAF-MHNN) model.
• To develop a robust image encryption scheme utilizing the MBPAF-MHNN.

Main Methods:

• Design of a mixed-bipower activation function (MBPAF).
• Development of a MBPAF-Memristive Hopfield Neural Network (MBPAF-MHNN) model.
• Numerical analysis and FPGA implementation for dynamic validation.
• Design of a "Diffusion-Permutation-Diffusion" image encryption scheme with DNA operations.

Main Results:

• The MBPAF enables the MHNN to generate complex hyper-chaotic behaviors.
• Numerical simulations confirmed the complex dynamics of the MBPAF-MHNN model.
• FPGA implementation verified the model's feasibility and performance.
• The proposed encryption scheme demonstrated robustness and effectiveness.

Conclusions:

• The MBPAF is effective in inducing complex hyper-chaotic dynamics in MHNNs.
• The MBPAF-MHNN model provides a foundation for advanced chaotic systems.
• The developed image encryption scheme offers a secure and efficient solution for data protection.