Competing of Sznajd and voter dynamics in the Watts-Strogatz network

TL;DR

This paper studies how competing Sznajd and voter dynamics influence opinion spread on Watts-Strogatz networks, revealing abrupt changes in node states depending on rewiring probability and network clustering.

Contribution

It introduces a model combining Sznajd and voter dynamics on Watts-Strogatz networks, analyzing how clustering affects opinion dynamics and phase transitions.

Findings

Increased clustering favors Sznajd activation for small rewiring probabilities.

The concentration of S-nodes exhibits abrupt transitions at critical probabilities.

Network structure significantly influences the dominance of opinion dynamics.

Abstract

We investigate the Watts-Strogatz network with the clustering coefficient C dependent on the rewiring probability. The network is an area of two opposite contact processes, where nodes can be in two states, S or D. One of the processes is governed by the Sznajd dynamics: if there are two connected nodes in D-state, all their neighbors become D with probability p. For the opposite process it is sufficient to have only one neighbor in state S; this transition occurs with probability 1. The concentration of S-nodes changes abruptly at given value of the probability p. The result is that for small p, in clusterized networks the activation of S nodes prevails. This result is explained by a comparison of two limit cases: the Watts-Strogatz network without rewiring, where C=0.5, and the Bethe lattice where C=0.