Stability and Hopf Bifurcation Analysis of a Delayed Innovation Diffusion Model with Intra-Specific Competition

Author:

Kumar Rakesh1ORCID,Sharma Anuj Kumar2

Affiliation:

1. Department of Applied Sciences, Shaheed Bhagat Singh State University, Ferozepur, Punjab-152004, India

2. Department of Mathematics, LRDAV College, Jagraon, Ludhiana, Punjab-142026, India

Abstract

This article is concerned with the diffusion of a sport in a region, and the innovation diffusion model comprising of population classes, viz. nonadopters class, information class and adopters class. A qualitative analysis is carried out to assess the global asymptotic stability of the interior equilibrium for null delay. It has also been proved that the parameter [Formula: see text] (age gaps among sportspersons) in the intra-specific competition between the new players and the senior players can even destabilize the otherwise globally stable interior equilibrium state and the coexistence of all the populations is possible through periodic solutions due to Hopf bifurcation. With the help of normal form theory and center manifold arguments, the stability of bifurcating periodic orbits is determined. Numerical simulations have been executed in support of the analytical findings.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

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