A model is developed for the investigation of an enzymatic diffusion-reaction system. The aim is to analyze the dynamic behavior of three different species, the modification of their enzymatic kinetic properties and the existence of complex behaviors resulting of the catalytic activity induced by immobilization of acetylcholinesterase into artificial membrane enzymatically inactive. We report results that make possible the characterization and prediction of complex behaviors as well as a qualitative/quantitative analysis of the system stability via bifurcation diagram which allows to study: i) the effect of the initial substrate concentration in the reservoir and ii) the effect of reaction-permeation modulus of the membrane as bifurcation parameters.