Memristive electromagnetic induction effects on Hopfield neural network

Due to the existence of membrane potential differences, the electromagnetic induction flows can be induced in the interconnected neurons of Hopfield neural network (HNN). To express the induction flows, this paper presents a unified memristive HNN model using hyperbolic-type memristors to link neurons. By employing theoretical analysis along with multiple numerical methods, we explore the electromagnetic induction effects on the memristive HNN with three neurons. Three cases are classified and discussed. When using one memristor to link two neurons bidirectionally, the coexisting bifurcation behaviors and extreme events are disclosed with respect to the memristor coupling strength. When using two memristors to link three neurons, the antimonotonicity phenomena of periodic and chaotic bubbles are yielded, and the initial-related extreme events are emerged. When using three memristors to link three neurons end to end, the extreme events owning prominent riddled basins of attraction are demonstrated. In addition, we develop the printed circuit board (PCB)-based hardware experiments by synthesizing the memristive HNN, and the experimental results well confirm the memristive electromagnetic induction effects. Certainly, the PCB-based implementation will benefit the integrated circuit design for large-scale Hopfield neural network in the future.

Automated summary

This paper explores the electromagnetic induction effects on memristive HNN with theoretical analysis and numerical methods, discussing various bifurcation behaviors, chaotic phenomena, and extreme events based on different neuron linkage configurations. Hardware experiments confirm the electromagnetic induction effects, demonstrating the potential benefits for future integrated circuit design of large-scale Hopfield neural networks.