Transient Bimodality in Innovation Diffusion: A Refined Mathematical Approach and Case Studies
Keywords:
Innovation Diffusion, Transient Bimodality, Extended Bass Model, Mathematical Modeling, Adoption Dynamics, Stochastic Analysis, Social NetworksAbstract
Innovation diffusion is conventionally modeled as a unimodal process, capturing the pro-gression of adoption from innovators to the majority and ultimately to laggards. However, empirical observations and theoretical developments increasingly highlight the occurrence of transient bimodality, wherein the adoption trajectory briefly displays a two-peak pattern. This paper refines the Extended Bass Model to rigorously examine the transiently bimodal diffusion phenomenon and elucidates the role of population heterogeneity, stochastic param-eters, and social network effects in driving such behavior. We provide detailed mathematical derivations of equilibrium points, stability analysis, and conditions under which transient bi-modality emerges. Moreover, through illustrative case studies on emerging technologies and sustainable innovations, we offer empirical validation and managerial insights for harnessing transient bimodality to optimize marketing, policy, and resource-allocation strategies. Our findings demonstrate that recognizing and strategically leveraging transient bimodality can expedite innovation adoption while minimizing market uncertainties, thus offering a robust framework for researchers and practitioners in the domain of innovation diffusion.
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