Bifurcations Of Microbial Continuous Culture Model With Restrained Microbial Growth Rate

As is known to us, microbial growth rate plays an important role in the process of micro-bial continuous culture. In this paper, a three dimensional microbial continuous culture model is considered to study the impact of restrained microbial growth rate function μ. Different from the classical microbial growth rate function of Monod, we suppose that both excess substrat and excess product will restrain the growth of microbe. In this case, the system becomes more reasonable and its dynamical behaviour has extremely changed. By analysing the coefficients of the model, we can prove the existence of the equilibria and study the different types of singularities. The system has no more than two nontriv-ial equilibrium points. The trivial equilibrium point Eo will change its stability with the changing of the parameter. We prove that the model will undergo transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation at nontrivial equilibrium point. Numerical simulation is built to verify the occurrence of Hopf bifurcation. We also present the details of computing the first Lyapunov coefficient li of the system.