Stability and Bifurcation Analysis of the Nutrient-Microorganism Model

Abstract

Stability analysis and bifurcation of the nutrient-microorganism model are presented in this paper. It is found that the model could experience the changes of the equilibrium points and the saddle-node, the Hopf and the codimension-2 Bogdanov-Takens bifurcations. The induced complex dynamics are also illustrated, by virtue of theory like the Sotomayor’s theorem, the normal form and the universal unfolding. From the obtained results, some insights into interaction between the nutrient and the microorganism can be given. Further, numerical simulation is carried out to verify the theoretical results.