Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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AN INNOVATION DIFFUSION MODEL IN PARTIAL COMPETITIVE AND COOPERATIVE MARKET: ANALYSIS WITH TWO INNOVATIONS

  • CHUGH, S. (Department of Mathematics, Dayanand Mathra College) ;
  • GUHA, R.K. (Department of Mathematics, Sant Longowal Institute of Engineering & Technology) ;
  • DHAR, JOYDIP (Department of Applied Science, ABV-Indian Institute of Information Technology and Management Gwalior)
  • Received : 2021.10.19
  • Accepted : 2022.03.07
  • Published : 2022.03.30
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Abstract

An innovation diffusion model is proposed model consists of three classes, namely, a non-adopter class, adopter class innovation-I, and adopter class innovation-II in a partially competitive and cooperative market. The proposed model is analyzed with the help of the qualitative theory of a system of ordinary differential equations. Basic influence numbers associated with first and second innovation $R_{0_1}$ and $R_{0_2}$ respectively in the absence of each other are quantified. Then the overall basic influence number (R0) of the system is assessed for analyzing stability in the market in different situations. Sensitivity analysis of basic influence numbers associated with first and second innovation in the absence of each other is carried out. Numerical simulation supports our analytical findings.

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