This paper takes a system dynamic approach to study homogeneous texts where the dynamics of the lexical richness of such texts over time are of the focal concern. It is hypothesized that the progress of the lexical complexity is driven by how far away this process is from the maximum level of complexity, while is subject to the fluctuations due to the dynamic nature of the system. It is shown that the lexical dynamics of homogeneous texts can be effectively modeled by a stochastic differential equation with proper upper bounds. The linguistic validity and the statistical goodness of the model are empirically tested with the texts of CGWR. Given the ubiquity of the diffusion phenomena in various settings of language and linguistic studies (e.g. language development), the findings of the current work should provide a useful methodological reference in comparison to classic approaches such as statistical regressions.