As new payment systems emerge, it is important to predict their dynamics and separate payments from speculative transactions. Based on the classification of payment systems as ‘one-sided’ and ‘two-sided’ we use mathematical methods to predict their behavior over time. By introducing the fatigue factor and involvement factor, we draw the differential equation that could be used for the analysis of the payment systems’ behavior. The analysis shows that any changes in the initial state of the system fade over time; one-time circumstantial changes (such as sudden regulatory change or promotional campaign) have an only temporary effect. Our equations can also be used to identify the prevailing type of transactions (P2P or C2B) in ‘mixed’ systems. Our model is verified by empirical data from payment card statistics, WebMoney registration rate and can be used to analyze Bitcoin usage as well. Further, research on using the model to explain and predict the competitive effects is also proposed. This is the first attempt at using differential equations for payment system analysis with a model verified by empirical evidence.