Stochastic evolution of innovation diffusion in heterogeneous groups: Study of life cycle patterns

A theoretical framework has been proposed to study patterns of innovation diffusion in a heterogeneous population, with applicability to a number of problem areas including marketing. The heterogeneity in the population is captured through randomly varying parameters, which have been modelled in terms of two-point distributions. The effect of heterogeneity leads to the generation of bi-modal life cycle patterns besides the conventional uni-modal pattern resulting from S-shaped curve. The stochastic evolution of the mean and variance of the number of adopters is found to depict a high level of relative fluctuation around the point of inflexion. As a result of randomness in parameters, the resulting differential equation for the evolution of the mean of the adoption process is characterized by a non-autonomous system having parameters which are no longer constant but become time dependent. For demonstrating the effectiveness of the proposed framework, a real data set which depicts a bi-modal life cycle curve is investigated. The fit is found to be extremely good while capturing appropriate product life cycle curve.