Two competitive products diffusion in heterogeneous consumer social networks with repeat purchase

Qiwei Huang,Yulin Zhang

doi:10.1186/s13662-019-2252-8

Abstract

This paper studies the dynamics of two competitive products diffusion in heterogeneous consumer social networks with repeat purchase. We demonstrate a threshold for the diffusion rate above which a single product can persistently diffuse in heterogeneous consumer social networks without considering advertising strategy if the other product fails to diffuse, and there exists a unique positive equilibrium state where two competitive products coexist and persistently diffuse in heterogeneous consumer social networks without considering advertising strategy. We also prove that there exists at least one positive equilibrium state where two products coexist and persistently diffuse in heterogeneous consumer social networks if considering advertising strategy. The numerical simulations show that the higher the average degree of heterogeneous consumer social networks, the faster the two competitive products diffuse, and the shorter the time required to reach the stable state.

Highlights

Social network plays a significant role in product diffusion
The heterogeneity of the network structure should be considered when we study product diffusion in consumer social networks, and studying the dynamics of product diffusion in consumer social networks is an important complement to the existing product diffusion theory
> 1, there exists only one positive eigenvalue, which means that system (1) has a unique positive equilibrium solution which guarantees that product 1 persistently diffuses in the heterogeneous consumer social network

Summary

Introduction

Social network plays a significant role in product diffusion. Consumers use social networks to transmit product information to influence other consumers’ decisions [1]. 2. If R0 > 1, system (1) has a unique positive equilibrium solution which guarantees that product 1 could persistently diffuse in the heterogeneous consumer social network.

Results

Conclusion