Real-time collision-free path planning and tracking control of a nonholonomic mobile robot in a dynamic environment is investigated using a neural dynamics based approach. The real-time robot path is generated through a dynamic neural activity landscape of a topologically organized neural network that represents the changing environment. The dynamics of each neuron is characterized by an additive neural dynamics model. The real-time tracking velocities are generated by a novel non-time based controller, which is based on the conventional event based control technique and an additive model. The effectiveness and efficiency of this approach are demonstrated through simulation and comparison studies.