Abstract
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.
Highlights
Memristor, a known nonlinear circuit element, is defined by Leon O
Using the threshold hyperbolic-type memristors to link the interconnected neurons, this paper presented a unified memristive Hopfield neural network (HNN) model to simulate electromagnetic induction effects
The uniform boundedness of the unified memristive HNN model was deduced in theory, proving that all the motions are trapped into a bounded region
Summary
A known nonlinear circuit element, is defined by Leon O. Electromagnetic induction flows can be induced when membrane potential differences are existed between each two interconnected neurons, whose effects are equivalent to the bidirectional induced currents emerged by a flux-controlled memristor linking each two neurons [8, 18, 19]. When considering the membrane potential difference between two interconnected neurons in HNN, a memristive HNN model with the electromagnetic induction was raised. The authors of the manuscript [30, 31] have discussed a memristive HNN model with two neurons under the action of electromagnetic induction, where coexisting behaviors triggered by different initial conditions were revealed and were validated by hardware experiments. It is necessary to establish a unified memristive HNN model to express the electromagnetic induction effects roundly, which has not been reported until now.
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