[논문]AN INNOVATION DIFFUSION MODEL IN PARTIAL COMPETITIVE AND COOPERATIVE MARKET: ANALYSIS WITH TWO INNOVATIONS

CHUGH, S.; GUHA, R.K.; DHAR, JOYDIP

doi:10.23091/japm.2022.027

AN INNOVATION DIFFUSION MODEL IN PARTIAL COMPETITIVE AND COOPERATIVE MARKET: ANALYSIS WITH TWO INNOVATIONS

Journal of applied and pure mathematics, v.4 no.1/2, 2022년, pp.27 - 36

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)

Abstract ▼ AI-Helper

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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표/그림 (7)

그림 FIGURE 1. Schematic flow competitive product
$TABLE 1. The sensitivity indices <TEX>$\gamma^{R_{0_1}}_{y_j}=\frac{{\partial}R_{0_1}}{{\partial}y_j}{\times}\frac{y_j}{R_{0_1}}$</TEX> of the basic influence number <TEX>$R_{0_1}$</TEX> to the values of various parameters <TEX>$y_j$</TEX>, are given in the following table$ 표 TABLE 1. The sensitivity indices $\gamma^{R_{0_1}}_{y_j}=\frac{{\partial}R_{0_1}}{{\partial}y_j}{\times}\frac{y_j}{R_{0_1}}$ of the basic influence number $R_{0_1}$ to the values of various parameters $y_j$, are given in the following table
표 TABLE 2. Values of different parameters
표 TABLE 3. Stable of equilibrium w.r.t. R_0₁ , R_0₂
그림 FIGURE 2. Population densities corresponds to Adopter-free Equilibrium
그림 FIGURE 3. Population densities corresponds to Adopter-I Dominating Equilibrium
그림 FIGURE 4. Population densities corresponds to Adopter-II Dominating Equilibrium

참고문헌 (19)

F.M. Bass, A new product growth model for consumer durable, Manage. Sci. 15 (1969), 215-227.
R. Tuli, J. Dhar, H.S. Bhatti, Innovation diffusion model with interactions and delays in adoption for two competitive products in two different patches, Ricerche di Matematica 68 (2019), 705-726.

상세보기
R. Tuli, J. Dhar, H.S. Bhatti, Sustaining of two competing products under the impact of the media including the experience of adopters, Journal of Applied Mathematics and Computing 60 (2019), 343-367.

상세보기
R. Kumar, A.K. Sharma, G.P. Sahu, Dynamical Behavior of an Innovation Diffusion Model with Intra-Specific Competition between Competing Adopters, Acta Math. Sci. (2021). https://doi.org/10.1007/s10473-022-0120-1

상세보기
E.M. Rogers, Diffusion of innovation, (3rd edition), The Free Press, 1995.
J. Dhar, M. Tyagi, P. Sinha, Dynamical Behavior in an Innovation Diffusion Marketing Model with Thinker Class of Population, International Journal of Business Management Economics and Research 1 (2010), 79-84.
W. Wang, P. Fergola, S. Lombardo, G. Mulone, Mathematical Models of Innovation Diffusion with Stage Structure, Applied Mathematical Modelling 30 (2006), 129-146.

상세보기
R. Kumar, A.K. Sharma, K. Agnihotri, Stability and Bifurcation Analysis of a Delayed Innovation Diffusion Model, Acta Mathematica Scientia 38B (2018), 709-732.
Y. Yu, W. Wang, Y. Zhang, An Innovation Diffusion Model for Three Competitive Products, Computers and Mathematics with Applications 46 (2003), 1473-1481.

상세보기
D.C. Jain, R.C. Rao, Effect of price on the demand for durables: Modeling, estimation and findings, J. Bus. Econ. Stat. 8 (1990), 163-170.

상세보기
J.M. Jones, C.J. Ritz, Incorporating distribution into new product diffusion models, Int. J. Res. Mark. 8 (1991), 91-112.
S.J. Lee, D.J. Lee, H.S. Oh, Technological Forecasting at the Korean Stock Market: A Dynamics Competition Analysis Using Lotka-Volterra Model, Technol. Forecast. Soc. Change 72 (2005), 1044-1057.
R. Tuli, J. Dhar, H.S. Bhatti, H. Singh, Dynamics Response by the Instant Buyer and Thinker Buyer in an Innovation Diffusion Marketing Model with Media Coverage, J. Math. Comput. Sci 76 (2017), 1022-1045.
R. Tuli, J. Dhar, H.S. Bhatti, An economic group model for innovation diffusion of new product with delay of adoption for low income group, J. Mathematical Modeling 7 (2019), 117-132.
R. Tuli, J. Dhar, H.S. Bhatti, A stage-structured model with media effect for innovation diffusion of new product, Inter. J. Pure and Applied Mathematics 119 (2018), 559-571.
J. Dhar, M. Tyagi, P. Sinha, An Innovation Diffusion Model for the Survival of a Product in a competitive Market: Basic influence Numbers, Inter. J. Pure and Applied Mathematics 89 (2013), 439-448.
J. Dhar, M. Tyagi, P. Sinha, Three simultaneous innovations interrelationships: An adopter dynamics model, Inter. J. Modeling, Simulation, and Scientific Computing 6 (2015), 1550031.
G.P. Sahu, Dhar, J. Analysis of an SVEIS epidemic model with partial temporary immunity and saturation incidence rate, Appl. Math. Model. 36 (2012), 908-923.

상세보기
P. Van den Driwssche, J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), 29-48.

상세보기

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