Nonlinear Diffusion for Bacterial Traveling Wave Phenomenon

The bacterial traveling waves observed in experiments are of pulse type which is different from the monotone traveling waves of the Fisher–KPP equation. For this reason, the Keller–Segel equations are widely used for bacterial waves. Note that the Keller–Segel equations do not contain the population...

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Bibliographic Details
Published in:Bulletin of mathematical biology 2023-05, Vol.85 (5), p.35-35, Article 35
Main Authors: Kim, Yong-Jung, Mimura, Masayasu, Yoon, Changwook
Format: Article
Language:English
Subjects:
Analysis
Bacteria
Cell Biology
Chemotaxis
Diffusion
Life Sciences
Mathematical analysis
Mathematical and Computational Biology
Mathematical Concepts
Mathematical Modelling
Mathematics
Mathematics and Statistics
Models, Biological
Original Article
Population dynamics
Population growth
Simulation of Biological Systems in memory of Masayasu Mimura
Traveling waves
Wave propagation
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Summary:The bacterial traveling waves observed in experiments are of pulse type which is different from the monotone traveling waves of the Fisher–KPP equation. For this reason, the Keller–Segel equations are widely used for bacterial waves. Note that the Keller–Segel equations do not contain the population dynamics of bacteria, but the population of bacteria multiplies and plays a crucial role in wave propagation. In this paper, we consider the singular limits of a linear system with active and inactive cells together with bacterial population dynamics. Eventually, we see that if there are no chemotactic dynamics in the system, we only obtain a monotone traveling wave. This is evidence that chemotaxis dynamics are needed even if population growth is included in the system.
ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-023-01138-3