In this work, the aim is to study the diffusion of innovation of two competing products. The main focus has been to understand the effects of the competitive dynamic market on the diffusion of innovation. The global smartphone operating system sales are chosen as an example. The availability of the sales and the number of users data, as well as the predictions for the future number of users, make the smartphone diffusion a new laboratory to test the innovation of diffusion models for the competitive markets. In this work, the Bass model and its extensions which incorporate the competition between the brands are used. The diffusion of smartphones can be considered on two levels: the product level and the brand level. The diffusion of the smartphone as a category is studied by using the Bass equation (category-level diffusion). The diffusion of each competing operating system (iOS and Android) are considered as the competition of the brands, and it is studied in the context of competitive market models (product-level diffusion). It is shown that the effects of personal interactions play the dominant role in the diffusion process. Moreover, the volume of near future sales can be predicted by introducing appropriate dynamic market potential which helps to extrapolate the model results for the future.