Dopamine is a critical neurotransmitter for the normal functioning of the central nervous system. Abnormal dopamine signal transmission in the brain has been implicated in diseases such as Parkinson's disease (PD) and schizophrenia, as well as in various types of drug addition. It is therefore important to understand the dopamine signaling dynamics in the presynaptic neuron of the striatum and the synaptic cleft, where dopamine synthesis, degradation, compartmentalization, release, reuptake, and numerous regulatory processes occur. The biochemical and biological processes governing this dynamics consist of interacting discrete and continuous components, operate at different time scales, and must function effectively in spite of intrinsic stochasticity and external perturbations. Not fitting into the realm of purely deterministic phenomena, the hybrid nature of the system requires special means of mathematical modeling, simulation and analysis. We show here how hybrid functional Petri-nets (HFPNs) and the software Cell Illustrator^® facilitate computational analyses of systems that simultaneously contain deterministic, stochastic, and delay components. We evaluate the robustness of dopamine signaling in the presence of delays and noise and discuss implications for normal and abnormal states of the system.