Dynamic Analysis, FPGA Implementation and Application of Memristive Hopfield Neural Network with Synapse Crosstalk

In a biological nervous system, neurons are connected to each other via synapses to transmit information. Synaptic crosstalk is the phenomenon of mutual interference or interaction of neighboring synapses between neurons. This phenomenon is prevalent in biological neural networks and has an important impact on the function and information processing of the neural system. In order to simulate and study this phenomenon, this paper proposes a memristor model based on hyperbolic tangent function for simulating the activation function of neurons, and constructs a three-neuron HNN model by coupling two memristors, which brings it close to the real behavior of biological neural networks, and provides a new tool for studying complex neural dynamics. The intricate nonlinear dynamics of the MHNN are examined using techniques like Lyapunov exponent analysis and bifurcation diagrams. The viability of the MHNN is confirmed through both analog circuit simulation and FPGA implementation. Moreover, an image encryption approach based on the chaotic system and a dynamic key generation mechanism are presented, highlighting the potential of the MHNN for real-world applications. The histogram shows that the encryption algorithm is effective in destroying the features of the original image. According to the sensitivity analysis, the bit change rate of the key is close to 50% when small perturbations are applied to each of the three parameters of the system, indicating that the system is highly resistant to differential attacks. The findings indicate that the MHNN displays a wide range of dynamical behaviors and high sensitivity to initial conditions, making it well-suited for applications in neuromorphic computing and information security.