In this paper, we investigate a nutrient–microorganism model with density-dependent motility in the sediment. We first establish the global existence and boundedness of classical solutions in a two-dimensional bounded domain. We then analyze the local stability of the spatially homogeneous interior steady state. Moreover, we derive conditions for the nonexistence and existence of nonconstant steady states. Furthermore, we study the local and global bifurcation structure and the stability of the resulting nonconstant steady states. In addition, we obtain the existence of nontrivial time-periodic solutions. Finally, numerical simulations are presented to illustrate and complement the theoretical results.
Lian et al. (Fri,) studied this question.
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