A two-compartment model of an enzyme system with substrate inhibition kinetics and hydrogen ion production is investigated. The model is used to study the bifurcation, instability, and chaotic behavior of the system. The investigation, although in a restricted region of the parameters’ space, has uncovered a good part of the rich dynamic characteristics of this system, including : period doubling sequences leading to chaos, banded chaos, fully developed chaos, interior crisis, tangent bifurcation leading to intermittency, periodic windows interrupting chaotic regions, and alternating periodic chaotic sequences. The results relate to the phenomena occurring in physiological experiments, such as the periodic stimulation of neural cells and the voltage-gated ion channel dynamics.