Non-Linear Diffusion Dynamics with Variable Market Capacity
Resumo
Thediffusionoftechnologicalinnovationstendstobehinderedbymarketsaturation,competitive
forces, andeconomicobstacles. Classical diffusionmodels, suchas theBassmodel, havebeeneffective in
modellingtheadoptionpatternofnewtechnologies. Thesemodels,however, tendtoassumeafixedmarket sizeandignoretheimpactofpolicyinterventions.Thisworkproposesamodifieddiffusionmodel thattakes
intoaccounttheeffectofgovernmentsubsidiesonincreasingthepotentialmarket.Byformulatingthesubsidy
effectasatime-varyinggrowthintheadopterpopulation,thepaperillustrateshowsubsidieshastenadoption.
Throughnumerical simulationsandexampleapplications tomarkets likeelectricvehicles, solarpower, and
energy-efficient appliances, themodel displays highcorrespondencewithactual trends. The results offer
policymakers important guidance in their efforts to encourage innovationadoptionbymeans of strategic
financial incentives
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of Forecasting 6 (1) (1987) 1–19.
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Journal of Marketing 54 (1) (1990) 1–26.
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(15) (1978) 1589–1597.
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(1) (2015) 214–236.
26. Melnikov, O., Zhao, X., Pricing and diffusion of durable goods with learning and network effects, Journal of Economic
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30. Rogers, E.M., Diffusion of Innovations, Free Press, New York, 1962.
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32. Sharif, M.N., Ramanathan, K., Binomial innovation diffusion models with dynamic potential adopter populations,
Technological Forecasting and Social Change 20 (1) (1981) 63–87.
33. Stremersch, S., Tellis, G.J., Understanding and managing international growth of new products, International Journal
of Research in Marketing 21 (4) (2004) 421–438.
(1975) 603–622.
2. Albernini, A., Bigano, M., How effective are energy-efficiency incentives?, Energy Economics 68 (2017) 413–428.
3. Bass, F.M., A new product growth model for consumer durables, Management Science 15 (5) (1969) 215–227.
4. Bassamboo, A., ¨ Ormeci, S., Market expansion dynamics in diffusion-driven demand models, Omega 52 (2015) 21–32.
5. Beck, T., Goldschmidt, M., Government incentives and clean technology diffusion, Energy Policy 141 (2020) 111442.
6. Bitencourt, L., Goldemberg, J., Bazzo, W.A., Bass diffusion model adaptation considering public policies applied to
electric vehicle diffusion, Energies 14 (17) (2021) 5435.
7. Danaher, P.J., Hardie, B.G.S., Putsis, W.P., Marketing-mix variables and the diffusion of successive generations of a
technological innovation, Journal of Marketing Research 38 (4) (2001) 501–514.
8. Decker, M., H¨ulsenberg, A., Consumer acceptance of innovations with network externalities, Technovation 34 (4) (2014)
220–231.
9. Dodson, J.A., Muller, E., Models of new product diffusion through advertising and word-of-mouth, Management Science
24 (15) (1978) 1568–1578.
10. Domarchi, C., Fiorello, D., Fontes, T., Electric vehicle forecasts: A review of models and methods, Transport Reviews
43 (5) (2023) 623–650.
11. Eskinasi, L., Diffusion of innovation theory and nonlinear dynamics, Technological Forecasting and Social Change 69
(2) (2002) 123–135.
12. Fan, R., Liu, G., Wang, Y., Wang, J., How do government policies affect the diffusion of green innovation?, Journal of
Cleaner Production 373 (2022) 133803.
13. Goldenberg, J., Libai, B., Muller, E., Talk of the network: A complex systems approach to word-of-mouth, Marketing
Letters 12 (3) (2001) 211–223.
14. Guidolin, M., Innovation diffusion processes: Concepts, models, and empirical evidence, Annual Review of Statistics
and Its Application 10 (2023) 397–423.
15. Guseo, R., Guidolin, M., Modelling a dynamic market potential: A class of automata networks for diffusion of innova
tions, Technological Forecasting and Social Change 76 (6) (2009) 806–820.
16. Guseo, R., Mortarino, C., Sequential market entries and competition modelling in multi-innovation diffusions, European
Journal of Operational Research 216 (3) (2012) 658–667.
17. Islam, T., Meade, N., The impact of attribute-based diffusion on forecasting accuracy, International Journal of Fore
casting 33 (3) (2017) 736–750.
18. Jiang, Z., Bass, F. M., & Bass, P. I. (2006). The Virtual Bass Model and the left-hand data-truncation bias in diffusion
of innovation studies. International Journal of Research in Marketing, 23(1), 93–106.
19. Kamakura, W.A., Long-term forecasting with innovation diffusion models: Impact of replacement purchases, Journal
of Forecasting 6 (1) (1987) 1–19.
20. Kamakura, W.A., Balasubramanian, S.K., Long-term view of the diffusion of durables: Role of price and adoption
influence, International Journal of Research in Marketing 5 (1) (1988) 1–13.
21. Kapur, P.K., Pham, H., Chanda, U., Kumar, S., Innovation diffusion model using stochastic differential equations,
International Journal of Operational Research 13 (2) (2012) 164–178.
22. Mahajan, V., A new product growth model with a dynamic market potential, Management Science 25 (11) (1979)
1027–1037.
23. Mahajan, V., Muller, E., Bass, F.M., New product diffusion models in marketing: A review and directions for research,
Journal of Marketing 54 (1) (1990) 1–26.
24. Mahajan, V., Peterson, R.A., Innovation diffusion in a dynamic potential adopter population, Management Science 24
(15) (1978) 1589–1597.
25. Melnikov, O., Demand theory of technological change and diffusion, Journal of Economics & Management Strategy 24
(1) (2015) 214–236.
26. Melnikov, O., Zhao, X., Pricing and diffusion of durable goods with learning and network effects, Journal of Economic
Theory 176 (2018) 1–38.
27. Mehta, S., Chaudhary, K., Kumar, P., Incorporating dynamic potential market in innovation diffusion using stochastic
differential equations, IEOM Conference (2019).
28. Parker, P.M., Incorporating competition into diffusion models, Management Science 38 (12) (1992) 1504–1516.
29. Parker, P.M., Aggregate diffusion forecasting models in marketing: A critical review, International Journal of Forecast
ing 9 (4) (1993) 447–466.
30. Rogers, E.M., Diffusion of Innovations, Free Press, New York, 1962.
31. Saviotti, P.P., Pyka, A., Economic development and diffusion of innovations, Structural Change and Economic Dynamics
15 (4) (2004) 519–540.
32. Sharif, M.N., Ramanathan, K., Binomial innovation diffusion models with dynamic potential adopter populations,
Technological Forecasting and Social Change 20 (1) (1981) 63–87.
33. Stremersch, S., Tellis, G.J., Understanding and managing international growth of new products, International Journal
of Research in Marketing 21 (4) (2004) 421–438.
Publicado
2026-04-11
Seção
Special Issue: Non-Linear Analysis and Applied Mathematics
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