Abstract: Memristor can enhance the nonlinearity of neural networks, promoting complex and diverse dynamic behaviors. This paper simulates external electromagnetic radiation in neural networks using a discrete memristor, constructing a new memristive neural network. Numerical analysis shows that, as parameters vary, the proposed network can undergo complex bifurcation processes, generating periodic, chaotic, and hyperchaotic attractors. Meanwhile, the network exhibits parameter-relied signal modulation behaviors, such as amplitude control and offset-boosting. As initial values change, the network can generate different types of extreme multistability. Furthermore, based on the proposed memristive neural network, this paper designs a new encryption algorithm for medical images, employing diagonal diffusion and triple-bit mutation methods to conceal image information. Relevant tests demonstrate that the algorithm can effectively protect the security of medical image information.