Stability analysis of a bioreactor model for biodegradation of xenobiotics

We consider an ecological model for biodegradation of toxic substances in aquatic and atmospheric biotic systems. The model, which is described by a nonlinear system of four ordinary differential equations, is known to be experimentally validated. We compute the equilibrium points of the model and study their asymptotic stability. Basic properties of the solutions like uniform boundedness and uniform persistence are established. Global asymptotic results are also developed. Numerical simulation results are presented to demonstrate the theoretical studies.