The recent application of new microfluidic technologies and methods has facilitated significant progress in the understanding of the fundamental mechanisms governing blood platelet function and how these parameters affect pathological thrombus formation. In-line with these new bioengineering approaches, the application of nonlinear dynamic systems analysis holds particular potential to extend our understanding of the complex interplay between mechanical and biochemical factors that underlie this complex biological phenomenon. In this paper we propose a simple mathematical model of the main dynamics of platelet aggregation/disaggregation observed experimentally in a novel microfluidic device that approximates a severe arterial stenosis. We apply dynamic systems theory (system identification) to explore the dynamics of the biomechanical platelet aggregation response to a range of shear stress rates, inhibiting blood-born chemical pathways of platelet activation (ADP, TXA2, and thrombin). We demonstrate that the proposed model is able to replicate experimental results with low variation, and suggest that the reduced set of model parameters has the potential to be used as a simplified way to evaluate the biomechanical dynamics of platelet aggregation. The proposed model has application to the development of automatic controllers within the context of microfluidic systems that may show great utility in the clinical assessment of platelet hyperfunction.