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A Discrete Velocity Kinetic Model with Food Metric: Chemotaxis Traveling Waves

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Abstract

We introduce a mesoscopic scale chemotaxis model for traveling wave phenomena which is induced by food metric. The organisms of this simplified kinetic model have two discrete velocity modes, \(\pm s\) and a constant tumbling rate. The main feature of the model is that the speed of organisms is constant \(s\,{>}\,0\) with respect to the food metric, not the Euclidean metric. The uniqueness and the existence of the traveling wave solution of the model are obtained. Unlike the classical logarithmic model case there exist traveling waves under super-linear consumption rates and infinite population pulse-type traveling waves are obtained. Numerical simulations are also provided.

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Acknowledgements

This research was supported by National Institute for Mathematical Sciences and National Research Foundation of Korea. S-H Choi is partially supported by NRF of Korea (No. 2015R1C1A1A02036611). Authors also thank to anonymous reviewers for valuable comments that improved this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics and the Institute of Natural Sciences, Kyung Hee University, Yongin, 446-701, South Korea

    Sun-Ho Choi

  2. Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, South Korea

    Yong-Jung Kim

  3. National Institute of Mathematical Sciences, 70 Yuseong-daero, Yuseong-gu, Daejeon, 305-811, South Korea

    Yong-Jung Kim

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  1. Sun-Ho Choi
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  2. Yong-Jung Kim
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Correspondence to Yong-Jung Kim.

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Choi, SH., Kim, YJ. A Discrete Velocity Kinetic Model with Food Metric: Chemotaxis Traveling Waves. Bull Math Biol 79, 277–302 (2017). https://doi.org/10.1007/s11538-016-0235-4

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  • DOI: https://doi.org/10.1007/s11538-016-0235-4

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