Dynamics of memristor coupled discrete fractional symmetric neural network model

Neural networks, also known as artificial neural networks (ANNs), represent innovative computational models inspired by the functioning of biological neurons in the human body. Currently, neural network models are employed to address intricate real-world challenges. This article focuses on constructing and dynamically analyzing interconnected symmetric neural network models inspired by the Hopfield type. These models incorporate discrete fractional memristor elements featuring quadratic memductance. The primary objective is to comprehend system characteristics by introducing nonlinearity to the inter-neuron weights in a functional manner. Additionally, the study explores the influence of electromagnetic radiation on neurons. Bifurcation diagrams, considering fractional order and Lyapunov exponents, illustrate the chaotic nature of the interconnected neural network model. The investigation delves into coexisting system states, examining coexisting bifurcations and attractors. The article offers potential for developing bio-inspired, energy-efficient, and adaptive neural network architectures, thereby contributing to advancements in artificial intelligence and neuromorphic applications.