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Topics in Mathematical Biology pp 301–337Cite as

Traveling Fronts

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Abstract

Every day plant and animal immigrants arrive at ports, railway and truck stations, and airports. Few of them are carried by individual passengers, most come with goods. There are seeds and insects in every load of iron ore, even more in lumber, grain, cotton, bananas, etc. Probably it is a futile attempt to control immigration except for large animal species.

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Notes

  1. 1.

    Foxes are typically territorial, but rabid foxes tend to migrate.

  2. 2.

    An integral equation v − a k ∗ v = f, with k ∗ 1 = 1 and a ∈ (0, 1), has the solution \(v = (1 + b\,\hat{k}{\ast})f\), where \(\hat{k} = ((1 - a)/a)\sum _{i=1}^{\infty }a^{i}k^{{\ast}i}\) is the normalized resolvent kernel and b = a∕(1 − a).

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Authors and Affiliations

  1. FB Biologie, Universität Tübingen, Tübingen, Germany

    Karl-Peter Hadeler

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Hadeler, KP. (2017). Traveling Fronts. In: Topics in Mathematical Biology. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-65621-2_8

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