Diversified Butterfly Attractors of Memristive HNN With Two Memristive Systems and Application in IoMT for Privacy Protection

Memristors are often used to emulate neural synapses or to describe electromagnetic induction effects in neural networks. However, when these two things occur in one neuron concurrently, what dynamical behaviors could be generated in the neural network? Up to now, it has not been comprehensively studied in the literature. To this end, this paper constructs a new memristive Hopfield neural network (HNN) by simultaneously introducing two memristors into one Hopfield-type neuron, in which one memristor is employed to mimic an autapse of the neuron and the other memristor is utilized to describe the electromagnetic induction effect. Dynamical behaviors related to the two memristive systems are investigated. Research results show that the constructed memristive HNN can generate Lorenz-like double-wing and four-wing butterfly attractors by changing the parameters of the first memristive system. Under the simultaneous influence of the two memristive systems, the memristive HNN can generate complex multi-butterfly chaotic attractors including multi-double-wing-butterfly attractors and multi-four-wing-butterfly attractors, and the number of butterflies contained in an attractor can be freely controlled by adjusting the control parameter of the second memristive system. Moreover, by switching the initial state of the second memristive system, the multi-butterfly memristive HNN exhibits initial-boosted coexisting double-wing and four-wing butterfly attractors. Undoubtedly, such diversified butterfly attractors make the proposed memristive HNN more suitable for chaos-based engineering applications. Finally, based on the multi-butterfly memristive HNN, a novel privacy protection scheme in the IoMT is designed. Its effectiveness is demonstrated through encryption tests and hardware experiments.