Stability and patterns of the nutrient-microorganism model with chemotaxis

In this paper, the stability and the bifurcations of the nutrient-microorganism model with chemotaxis are analyzed, subject to no-flux boundary conditions. By choosing the chemotaxis coefficient as the control parameter, it is found that the steady state bifurcation, the Hopf-Turing bifurcation, can happen in the model. The induced spatially homogeneous periodic solution, the non-constant steady state, and the spatially inhomogeneous periodic solution are exhibited. The results suggest that chemotaxis assimilated into the model could give rise to rich spatiotemporal dynamical behaviors.