Dynamics of a nutrient-microorganism model with density-dependent motility in the sediment

Key Points

• The study aims to explore the dynamics of a nutrient-microorganism model, focusing on motility and steady states.
• Establish global existence and boundedness of solutions in a two-dimensional domain
• Analyze local stability of the spatially homogeneous interior steady state
• Derive conditions for the existence and nonexistence of nonconstant steady states
• Investigate local and global bifurcation structure
• Perform numerical simulations to complement theoretical results
• Classical solutions exist globally and are bounded
• Conditions for the stability and existence of nonconstant steady states were identified
• Local and global bifurcation structures were developed
• Nontrivial time-periodic solutions were found
• Numerical simulations support the theoretical findings

Abstract