Three-dimensional m-HR neuron model and its application in medical image encryption

Theoretical research on neuronal dynamics is crucial for elucidating neural functions of the human brain, and electromagnetic fields significantly influence the electrical activity of neurons. This paper proposes a flux-controlled memristor and analyzes its frequency and amplitude dependent pinched hysteresis loops. Considering the electromagnetic induction effect of the memristor, a novel memristive Hindmarsh–Rose (m-HR) neuron model is constructed, which exhibits the coexistence of asymmetric hidden attractors. The theoretical analyses and simulation results on the Hamilton energy demonstrate that the energy evolution of the m-HR neuron model is predominantly associated with state variables. Subsequently, the intricate discharge patterns of the model are investigated through one-parameter and two-parameter bifurcation analysis, accompanied by complexity assessment. Based on the model, a medical image encryption scheme is devised, capable of simultaneously encrypting multiple images of arbitrary size and type. Additionally, the proposed cross-plane scrambling scheme can effectively minimize pixel correlation. Finally, the security tests indicate that the encryption scheme possesses high security and can effectively withstand diverse attacks.