Blood cell platelets form aggregates upon vessel wall injury. Under certain conditions, a disintegration of the platelet aggregates, called “reversible aggregation”, is observed in vitro. Previously, we have proposed an extremely simple (two equations, five parameters) ordinary differential equation-based mathematical model of the reversible platelet aggregation. That model was based on mass-action law, and the parameters represented probabilities of platelet aggregate formations. Here, we aimed to perform a nonlinear dynamics analysis of this mathematical model to derive the biomedical meaning of the model’s parameters. The model’s parameters were estimated automatically from experimental data in COPASI software. Further analysis was performed in Python 2.7. Contrary to our expectations, for a broad range of parameter values, the model had only one steady state of the stable type node, thus eliminating the initial assumption that the reversibility of the aggregation curve could be explained by the system’s being near a stable focus. Therefore, we conclude that during platelet aggregation, the system is outside of the influence area of the steady state. Further analysis of the model’s parameters demonstrated that the rate constants for the reaction of aggregate formation from existing aggregates determine the reversibility of the aggregation curve. The other parameters of the model influenced either the initial aggregation rate or the quasi-steady state aggregation values.