Multistability and Hidden Attractors in a Fractional-Order Memristive Tabu Learning Neuron Model and Its Medical Image Encryption

In order to simulate the transmission and processing of information with neurons, a memristor is used as a synapse, which has an electromagnetic induction effect. This paper proposed a fractional-order tabu learning neuron model with a memristor. Firstly, the analysis of the model's equilibrium points reveals the presence of hidden attractors. Secondly, the system is analyzed by bifurcation diagrams, Lyapunov exponent diagrams and phase diagrams, which is found to have a rich dynamic behaviors. The attraction basins demonstrate that the system is characterized by multistability. Additionally, the two-parameter bifurcation diagram accurately provides a description of the system's firing behavior with different parameter values. Finally, Based on the chaotic sequence, this paper designed a novel medical image encryption algorithm. The reliability of this algorithm is then theoretically analyzed.