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. (C) 2012 Elsevier Inc. All rights reserved.