Dynamic Study and Microcontroller Realization of a Single Fractional‐Order Hopfield Neuron Model Under Autapse and Electromagnetic Radiation Effects

ABSTRACT The initial Hopfield neural network (HNN) model, which emulates the nervous system, was conceived without considering the impact of some external effects such as electromagnetic phenomena. It used a resistor to mimic the self‐coupling synapse of the neuron. Due to their nonlinearity, modifiability, and nonvolatility, memristors can reproduce natural synapses with great precision. They can simulate the self‐coupling synapse of the neuron, as well as the effects of the electromagnetic phenomena on the neurons. In this work, we propose and study the dynamic behaviors of a memristive single fractional‐order Hopfield neuron (MSFHN) model with a self‐coupling synapse and affected by electromagnetic radiation. The stability of the stationary points is studied. The solutions of the model are carried out using one of the most efficient and reliable techniques called the Adomian decomposition method (ADM). The dynamic behaviors of the model are investigated based on the self‐coupling strength, the coupling strength between the membrane potential and the magnetic flux, the fractional order, and the initial conditions using common methods for characterizing dynamic systems. Numerical findings indicate that the proposed single fractional‐order neuron model exhibits a variety of intricate dynamics such as chaotic behavior, transient transitions, antimonotonicity, and initial boosting behavior. Numerical simulation results are validated with the microcontroller implementation of the MSFHN model.