Bifurcation behaviour of a nonlinear innovation diffusion model with external influences
type: Item
instance of: scholarly article
title: Bifurcation behaviour of a nonlinear innovation diffusion model with external influences
zbMATH Open document ID: 1474.37095
DOI: 10.1504/IJDSDE.2020.109107
author: Yanyan Li
published in: International Journal of Dynamical Systems and Differential Equations
publication date: 2021-04-22T00:00:00Z
review text: Summary: A nonlinear form of Bass model for innovation diffusion consisting of a system of two variables viz. for adopters and nonadopters population is proposed to lay stress on the evaluation period. The local stability of a positive equilibrium and the existence of Hopf bifurcation are demonstrated by analysing the associated characteristic equation. The critical value of evaluation period is determined beyond which small amplitude oscillations of the adopter and nonadopters population occur, and this critical value goes on decreasing with the increase in carrying capacity of the non-adopters population. The direction and the stability of bifurcating periodic solutions is determined by using the normal form theory and centre manifold theorem. It is observed that the cumulative density of external influences has a significant role in developing the maturity stage (final adoption stage) in the system. Numerical computations are executed to confirm the correctness of theoretical investigations.
Mathematics Subject Classification ID: 37L10
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 49Q12
zbMATH DE Number: 7336630
zbMATH Keywords: innovation diffusion model
zbMATH Keywords: evaluation period
zbMATH Keywords: variable external influences
zbMATH Keywords: word of mouth
zbMATH Keywords: stability analysis
zbMATH Keywords: sensitivity analysis
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: centre manifold theorem
zbMATH Keywords: normal form theory
Wikidata QID: Q110650050
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7336630