Abstract
Possible constitutive models are examined for the formation of a herd, under the assumption that a herd forms a travelling wave while grazing. Under quite general conditions, it is found that the only possibility for a travelling wave is a balance between food seeking and natural dispersion, such as in chemotaxis. The stability of the travelling wave previously conjectured, is shown both for one- and two-dimensional perturbations.
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References
Adler, J.: Chemotaxis in bacteria. Ann. Rev. Biochem. 44, 341–356 (1970).
Keller, E., Segel, L.: Travelling bands of chemotactic bacteria. A theoretical analysis. J. Theor. Biol. 30, 235–248 (1971)
Odell, G., Keller, E.: Travelling bands of chemotactic bacteria revisited. J. Theor. Biol. 56, 243–247 (1976)
Scribner, T., Segel, L., Rogers, E.: A numerical study of the formation and propagation of travelling bands of chemotactic bacteria. J. Theor. Biol. 46, 189–219 (1974)
Kennedy, C. R., Aris, R.: Travelling waves—A simple population model involving growth and death. Bull. Math. Biol. 42, 397–429 (1980)
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Gueron, S., Liron, N. A model of herd grazing as a travelling wave, chemotaxis and stability. J. Math. Biology 27, 595–608 (1989). https://doi.org/10.1007/BF00288436
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DOI: https://doi.org/10.1007/BF00288436