IMPACT OF INCENTIVE ON THE DIFFUSION OF AN INNOVATION: A MODELLING STUDY


By

Maninder Singh Arora

Department of Mathematics, PPN Postgraduate College, CSJM University, Kanpur-208001, Uttar Pradesh, India

Email:maninderarora120@gmail.com

(Received: December 05,2021; In format December 16,2021; Revised: December 27,2021; Accepted : May 24,2022)


Abstract

In this paper, an attempt is made to study the impact of positive incentive on the diffusion of an innovation in the society. For this purpose, a non-linear model is proposed involving the following three dependent variables- (i) the number of non-adopters (ii) the number of adopters and (iii) the variable cumulative incentive introduced to accumulate the rate of diffusion of an innovation. The model is analyzed by using stability theory of system of ordinary differential equations and numerical simulations. Although the core concept behind the model is based upon the approach of Bass model, yet we have incorporated a number of generalizations for the better adaptability of the model in the real market scenario. A dynamic market affected by demographical changes caused due to immigration, emigration, etc. has been considered. The coefficients of internal and external influence have also been considered to be variables depending linearly on the total market population and cumulative incentive, respectively. The analysis shows that the number of adopters increases with the increase in the external influence caused by cumulative incentive as a variable. It is also shown that incentive has stabilizing effect on the system. The results are illustrated by numerical simulations.


2020 Mathematical Sciences Classification: 30D15, 30A10

Keywords and Phrases: Diffusion models, spread of innovation, mathematical model, stability analysis, communication channels



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