Nonlinear dynamics and experimental realization of a piecewise linear multi-scroll Hopfield neural network with a memristive synapse
Luis Carlos Lujano-Hernández, Jesus Manuel Munoz-Pacheco, A. Sánchez-Gaspariano · Discrete and Continuous Dynamical Systems - S · 2025
This paper focuses on using piecewise linear (PWL) functions to generate continuous-discrete chaotic neural networks. Specifically, we examine a multi-scroll Hopfield neural network (HNN) composed of four neurons and incorporate a PWL memristor as a synapse in the second neuron. It means that we also utilize a PWL function as an activation function to replace the typical hyperbolic tangent function, a second PWL function to mimic a sine function, which controls the internal state of the memristor, and finally, a third PWL function to set the number of scrolls on the chaotic attractor. To investigate the mechanisms behind chaos generation, the dynamic behaviors of the proposed continuous-discrete Hopfield neural network are analyzed using equilibrium points, time series analysis, bifurcation diagrams, and Lyapunov exponents. Next, we demonstrate that the chaotic attractor of the proposed PWL HNN can be experimentally observed by field-programmable gate array (FPGA) technology using an optimized design that does not require multipliers. As a result of the optimized FPGA design, the proposed approach enables a straightforward physical implementation of PWL HNNs with less hardware utilization and a relatively high throughput compared to CORDIC– and DSP–based designs, which may enhance data processing capabilities