Transient Bimodality in Innovation Diffusion: A Mathematical and Empirical Exploration
Keywords:
Innovation Diffusion, Transient Bimodality, Extended Bass Model, Mathe-matical Modeling, Adoption Dynamics, Stochastic Analysis, Social NetworksAbstract
Innovation diffusion has traditionally been modeled using unimodal growth pat-terns, as epitomized by the Bass Model. However, both empirical observations and theoretical findings suggest that the adoption trajectory can exhibit transient bi-modality, whereby adoption follows two distinct peaks separated by a partial slow-down or temporary decline. This paper offers a mathematically rigorous study of such dynamics by extending the canonical Bass framework to incorporate popu-lation heterogeneity, stochastic parameters, and piecewise variable diffusion rates (PVRD). We develop an ODE-based model, derive conditions for the emergence of double-peaked solutions, and propose fitting strategies—including Simulated Annealing—to handle the resulting high-dimensional estimation problem. Through analytical insights, numerical illustrations, and real-world case studies in diverse domains (e.g., consumer durables, green technologies), we elucidate how transient bimodality arises, why it matters for strategic marketing and policy decisions, and what it implies for further research on innovation diffusion.
Downloads
References
Rogers, E. M. (2003). Diffusion of Innovations (5th ed.). Free Press.
Bass, F. M. (1969). A new product growth for model consumer durables. Management Science, 15(5), 215–227.
Mahajan, V., Muller, E., & Bass, F. M. (1991). New product diffusion models in marketing: A review and directions for research. Journal of Marketing, 54(1), 1–26.
Fischer, T., Truffer, B., & Markard, J. (2020). Green Diffusion: The Adoption, Diffu-sion, and Social Embedding of Sustainable Innovation. Annual Review of Environment and Resources, 45, 315–341.
Mahajan, V., & Peterson, R. A. (1990). Models for innovation diffusion. New York: Sage Publications.
Valente, T. W. (2008). Network Models of the Diffusion of Innovations. Computa-tional and Mathematical Organization Theory, 14(3), 201–224.
Mittal, B. (1998). Diffusion of New Products: Empirical Generalizations and Man-agerial Uses. Marketing Science, 17(2), 98–115.
Rogers, E. M. (1995). Diffusion of Innovations (4th ed.). Free Press.
Valente, T. W. (1995). Network Models of the Diffusion of Innovations. Computa-tional & Mathematical Organization Theory, 1(1), 57–77.
Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598), 671–680.
Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2019). Statistics for Business and Economics (9th ed.). Cengage Learning.
Greenhalgh, T., Robert, G., Macfarlane, F., Bate, P., & Kyriakidou, O. (2004). Diffusion of Innovations in Service Organizations: Systematic Review and Recom-mendations. The Milbank Quarterly, 82(4), 581–629.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
All papers should be submitted electronically. All submitted manuscripts must be original work that is not under submission at another journal or under consideration for publication in another form, such as a monograph or chapter of a book. Authors of submitted papers are obligated not to submit their paper for publication elsewhere until an editorial decision is rendered on their submission. Further, authors of accepted papers are prohibited from publishing the results in other publications that appear before the paper is published in the Journal unless they receive approval for doing so from the Editor-In-Chief.
IJISAE open access articles are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. This license lets the audience to give appropriate credit, provide a link to the license, and indicate if changes were made and if they remix, transform, or build upon the material, they must distribute contributions under the same license as the original.
