An innovation diffusion model for three competitive products
type: Item
instance of: scholarly article
title: An innovation diffusion model for three competitive products
zbMATH Open document ID: 1050.34071
DOI: 10.1016/S0898-1221(03)90184-2
author: Yumei Yu
author: Wendi Wang
author: Yong Zhang
publication date: 2004-09-23T00:00:00Z
review text: In this work, an innovation diffusion model describing the dynamics of 3 competing products is studied. When all competitors are using advertisement, a unique interior solution exists. It is shown to be globally asymptotically stable. When only two competitors are using advertisement, two equilibrium solutions are shown to exist: one interior and the other on the boundary. Conditions for each of them to be globally asymptotically stable are derived. When at most one of the competitors use advertisement, only boundary equilibrium solutions exist. Conditions for each of them to be globally asymptotically stable are derived. This work indicates that for the persistence of competitors in some cases advertisement is more important than people's contacts.
reviewed by: E. Ahmed
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 91B42
zbMATH DE Number: 2102407
zbMATH Keywords: innovation
zbMATH Keywords: diffusion
zbMATH Keywords: competition
zbMATH Keywords: global stability
Wikidata QID: Q110648861
MaRDI profile type: Publication
cites work: Introduction Strategy for New Products with Positive and Negative Word-of-Mouth
cites work: Q3812031
cites work: Q4487330
cites work: Stability of competitive innovation diffusion model
cites work: Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets
cites work: Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere
cites work: Systems of differential equations which are competitive or cooperative: III. Competing species
cites work: Systems of Differential Equations That are Competitive or Cooperative. IV: Structural Stability in Three-Dimensional Systems
cites work: Systems of differential equations that are competitive or cooperative. V: Convergence in 3-dimensional systems
cites work: Q4834372
cites work: On the Asymmetric May--Leonard Model of Three Competing Species
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2102407