Stability analysis for a mathematical model of the lac operon

Abstract

A mathematical model for induction of the lac operon is derived using biochemical kinetics and includes delays for transcription and translation. Local analysis of the unique equilibrium of this nonlinear model provides conditions for stability. Techniques are developed to determine Hopf bifurcations, and stability switching is found for the delayed system. Near a double bifurcation point a hysteresis of solutions to two stable periodic orbits is studied. Global analysis provides conditions on the model for asymptotic stability. The biological significance of our results is discussed.