Stability of a neural network model with small-world connections

TL;DR

This paper introduces a neural network model with weighted small-world connections, inspired by biological neural networks, and investigates its stability, addressing limitations of previous unweighted models.

Contribution

The paper presents a novel weighted small-world neural network model and analyzes its stability, bridging the gap between biological realism and network theory.

Findings

Weighted small-world networks better mimic biological neural connections

The stability conditions depend on the distribution of weights

Weighted models exhibit different dynamic behaviors than unweighted ones

Abstract

Small-world networks are highly clustered networks with small distances among the nodes. There are many biological neural networks that present this kind of connections. There are no special weightings in the connections of most existing small-world network models. However, this kind of simply-connected models cannot characterize biological neural networks, in which there are different weights in synaptic connections. In this paper, we present a neural network model with weighted small-world connections, and further investigate the stability of this model.