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Delay Induced Hopf Bifurcation in a Nonlinear Innovation Diffusion Model: External Influences Effect

Delay Induced Hopf Bifurcation in a Nonlinear Innovation Diffusion Model: External Influences Effect
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Year:    2018

East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 3 : pp. 422–446

Abstract

A nonlinear innovation diffusion model which incorporates the evaluation stage (time delay) is proposed to describe the dynamics of three population classes for non-adopter and adopter densities. The local stability of the various equilibrium points is investigated. It is observed that the system is locally asymptotically stable for a delay limit and produces periodic orbits via a Hopf bifurcation when evaluation period crosses a critical value. Applying normal form theory and center manifold theorem, we study the properties of the bifurcating periodic solutions. The model shows that the adopter population density achieves its maturity stage faster if the cumulative density of external influences increases. Several numerical examples confirm our theoretical results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.010417.200118

East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 3 : pp. 422–446

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Evaluation period stability analysis Hopf bifurcation normal form theory center manifold theorem.

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