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Aggregating pattern dynamics in a chemotaxis model including growth

Author

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  • Mimura, Masayasu
  • Tsujikawa, Tohru

Abstract

A population model including diffusion, chemotaxis and growth is studied. Assuming that the diffusion rate and the chemotactic rate are both very small compared with the growth rate, we derive a new equation to describe the time-evolution of the aggregating region of biological individuals and show the conditions for the existence and stability of radially symmetric equilibrium solutions of the equation, which indicate the aggregation of individuals.

Suggested Citation

  • Mimura, Masayasu & Tsujikawa, Tohru, 1996. "Aggregating pattern dynamics in a chemotaxis model including growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(3), pages 499-543.
    • Handle: RePEc:eee:phsmap:v:230:y:1996:i:3:p:499-543
    DOI: 10.1016/0378-4371(96)00051-9
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    References listed on IDEAS

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    1. Ian McLeod, 1977. "Derivation of the Theoretical Autocovariance Function of Autoregressive‐Moving Average Time Series," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(2), pages 194-194, June.
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    Cited by:

    1. Guo, Liujie & Gao, Fei & Zhan, Hui, 2022. "Existence, uniqueness and L∞-bound for weak solutions of a time fractional Keller-Segel system," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    2. Shengmao Fu & Fenli Cao, 2013. "Pattern Formation of a Keller-Segel Model with the Source Term," Journal of Mathematics, Hindawi, vol. 2013, pages 1-11, October.
    3. Willemsen, Jorge F., 2010. "Anomalous invasion in a 2d model of chemotactic predation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3484-3495.

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