Fractional-order bi-Hopfield neuron coupled via a multistable memristor: Complex neuronal dynamic analysis and implementation with microcontroller

Abstract

The Hopfield neuron is an artificial neuron model used for pattern memorization and recognition. It exhibits a complex dynamic with stable states corresponding to memorized patterns. In order to grasp a more complete representation of the information exchange between two neurons, emphasizing the importance of neuronal connections in brain processing, we propose in this work the coupling of two fractional-order Hopfield neurons via a fractional-order flux-controlled multistable memristor. Each of these two neurons incorporates a self-coupling memristive component, called an autapse memristor. Additionally, the second neuron is subjected to an external electromagnetic radiation, simulated by an additional memristor. The I-V characteristics of the memristors integrated in this model are analyzed through numerical simulations. The simulations of model dynamics versus its diverse parameters have revealed rich and complex dynamical behaviors. These simulations demonstrate that the proposed model generates a variety of homogeneous and heterogeneous chaotic attractors, distributed at diverse locations. The elaborated memristor coupled fractional-order bi-Hopfield neuron MCFBHN model is implemented on an Arduino-Due platform. A comparison of the results of the two approaches shows good consistency.