Two Adopter Dynamics with Cross Adoption: Effect of Adoption Delays

Two Adopter Dynamics with Cross Adoption

Abstract

The present study is aimed at analysing the reaction of people, how they react in the market towards the offer of two products where delay in adoption exists for both products. For this purpose, a three compartment model is proposed by classifying a population into three categories namely, non-adopter class, adopter class of product-I and produt-II. Boundedness, positivity and basic influence number of the mathematical model are analysed. Stability analysis for adopter free equilibrium and interior equilibrium is carried out for different cases on delay using Ruan's and Lin-Wang's stability theory. Sensitivity analysis is performed for the basic influence number. Numerical simulations of the present model have been carried out with the help of MATLAB, for supporting our analytical findings. As delay for first adopter increases, the system switches from unstable to stable state, whereas delay for the second adopter decreases, the system becomes stable.