Crowdfunding is a powerful tool for individuals or organizations seeking financial support from a vast audience. Despite widespread adoption, managers often lack information about dynamics of their platforms. Hawkes processes have been used to represent self-exciting behavior in a wide variety of empirical fields, but have not been applied to crowdfunding platforms in a way that could help managers understand the dynamics of users' engagement with the platform. In this paper, we extend the Hawkes process to capture important features of crowdfunding platform contributions and apply the model to analyze data from two donation-based platforms. For each user-item pair, the continuous-time conditional intensity is modeled as the superposition of a self-exciting baseline rate and a mutual excitation by preferential attachment, both depending on prior user engagement, and attenuated by a power law decay of user interest. The model is thus structured around two time-varying features -- contribution count and item popularity. We estimate parameters that govern the dynamics of contributions from 2,000 items and 164,000 users over several years. We identify a bottleneck in the user contribution pipeline, measure the force of item popularity, and characterize the decline in user interest over time. A contagion effect is introduced to assess the effect of item popularity on contribution rates. This mechanistic model lays the groundwork for enhanced crowdfunding platform monitoring based on evaluation of counterfactual scenarios and formulation of dynamics-aware recommendations.

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