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.

Automated summary

In this paper, the stability and bifurcations of the nutrient-microorganism model with chemotaxis under no-flux boundary conditions are analyzed. It is found that the presence of chemotaxis can lead to steady state bifurcation, namely Hopf-Turing bifurcation, in the model. The model exhibits induced spatially homogeneous periodic solution, non-constant steady state, and spatially inhomogeneous periodic solution. These results suggest that the inclusion of chemotaxis in the model can give rise to diverse spatiotemporal dynamical behaviors.