Bacterial chemotaxis without gradient-sensing. (English) Zbl 1339.92012
Chemotaxis models like the Keller-Segel system are based on spatial or temporal gradient measurements by individual organisms. The authors propose an explanation of the chemotactic behavior when individuals do not sense the gradient of chemical concentration. The model (in one space dimension) is based on the observation: if individuals increase their dispersal rate to find food when there is not enough food, an accurate chemotactic behavior may be obtained without sensing the gradient. Such a dispersal (suggested by E. Cho and the second author [Bull. Math. Biol. 75, No. 5, 845–870 (2013; Zbl 1311.92155)]) is called starvation driven diffusion. This model is similar to the original Keller-Segel model. Traveling waves are studied for that model.
Reviewer: Piotr Biler (Wrocław)
MSC:
| 92C17 | Cell movement (chemotaxis, etc.) |
| 35C07 | Traveling wave solutions |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 35K59 | Quasilinear parabolic equations |
| 35A24 | Methods of ordinary differential equations applied to PDEs |
Keywords:
chemotaxis; Keller-Segel equation; starvation driven diffusion; traveling waves; phase plane analysisCitations:
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