Dynamics and Implementation of FPGA for Memristor-Coupled Fractional-Order Hopfield Neural Networks

Abstract

The coupling between neurons can lead to diverse neural network architectures, with the Hopfield neural network (HNN) being particularly noteworthy for its resemblance to human brain function and its potential in modeling chaotic systems. This paper introduces a novel approach: a fractional-order HNN coupled with a hyperbolic tangent-type memristor. Initially, we propose a new model for the hyperbolic tangent-type memristor and fingerprints. Subsequently, we construct a memristor-coupled fractional-order Hopfield neural network (mFOHNN) and explore its dynamic behavior using various analytical tools, including phase diagrams, bifurcation diagrams, Lyapunov exponent diagrams, Poincaré maps, and attractor basins. Our findings reveal rich coexisting bifurcation behavior in the neural network model, influenced by different initial values of coexisting attractors. Finally, we validate the model through analysis and implementation using Multisim circuit simulation software and FPGA hardware, respectively.