Bifurcations and Spatiotemporal Patterns in the Diffusive Nutrient-Microorganism Model

In this paper, the diffusive nutrient-microorganism model subject to Neumann boundary conditions is considered. The Hopf bifurcations and steady state bifurcations which bifurcate from the positive constant equilibrium of the system are investigated in details. In addition, the formulae to determine...

Full description

Saved in:
Bibliographic Details
Published inActa Mathematicae Applicatae Sinica Vol. 41; no. 1; pp. 162 - 178
Main Authors Wang, Ya-di, Yuan, Hai-long, Li, Yan-ling
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2025
Springer Nature B.V
EditionEnglish series
Subjects
Applications of Mathematics
Boundary conditions
Hopf bifurcation
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Microorganisms
Orbits
Steady state models
Theoretical
35B32
nutrient-microorganism model
Hopf bifurcation
steady state bifurcation
35K57
simulations
Online AccessGet full text

Cover

More Information
Summary:In this paper, the diffusive nutrient-microorganism model subject to Neumann boundary conditions is considered. The Hopf bifurcations and steady state bifurcations which bifurcate from the positive constant equilibrium of the system are investigated in details. In addition, the formulae to determine the direction of Hopf and steady state bifurcations are derived. Our results show the existence of spatially homogeneous/nonhomogeneous periodic orbits and steady state solutions, which indicates the spatiotemporal dynamics of the system. Some numerical simulations are also presented to support the analytical results.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-024-1079-6