Global bifurcation and stability of steady states for a bacterial colony model with density-suppressed motility. (English) Zbl 1481.92089
Summary: We investigate the structure and stability of the steady states for a bacterial colony model with density-suppressed motility. We treat the growth rate of bacteria as a bifurcation parameter to explore the local and global structure of the steady states. Relying on asymptotic analysis and the theory of Fredholm solvability, we derive the second-order approximate expression of the steady states. We analytically establish the stability criterion of the bifurcation solutions, and show that sufficiently large growth rate of bacteria leads to a stable uniform steady state. While the growth rate of bacteria is less than some certain value, there is pattern formation with the admissible wave mode. All the analytical results are corroborated by numerical simulations from different stages.
MSC:
| 92C99 | Physiological, cellular and medical topics |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35K57 | Reaction-diffusion equations |
| 35K59 | Quasilinear parabolic equations |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
Keywords:
density-suppressed motility; reaction-diffusion model; global bifurcation; stability analysisReferences:
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