Dynamical properties of the reaction–diffusion type model of fast synaptic transport

The modulation of a signal that is transmitted in the nerve system takes place in chemical synapses. This article focuses on the phenomena undergone in the presynaptic part of the synapse. A diffusion–reaction type model based on the partial differential equation is proposed. Through an averaging procedure this model is reduced to a model based on ordinary differential equations with control, which is then analyzed according to its dynamical properties—controllability, observability and stability. The system is strongly connected to the one introduced by Aristizabal and Glavinovic (2004) [13]. The biological implications of the obtained mathematical results are also discussed.