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Group Dynamics of Phototaxis: Interacting Stochastic Many-Particle Systems and Their Continuum Limit

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

Listed:
  • D. Bhaya

    (Stanford University, Department of Plant Biology Carnegie Institution of Washington)

  • D. Levy

    (Stanford University, Department of Mathematics)

  • T. Requeijo

    (Stanford University, Department of Mathematics)

Abstract

In this chapter, we introduce new models for describing the motion of phototaxis, i.e., bacteria that move toward light. Following experimental observations, the first model describes the locations of bacteria, an internal property of the bacteria that is related to the group dynamics, and the interaction between the bacteria and the medium in which it resides. The second model is a new multiparticle system following the same quantities as in the first model. The main theorem shows how to obtain a new system of PDEs, which we refer to as the phototaxis system as the limit dynamics of the multiparticle system. Numerical simulations are provided.

Suggested Citation

  • D. Bhaya & D. Levy & T. Requeijo, 2008. "Group Dynamics of Phototaxis: Interacting Stochastic Many-Particle Systems and Their Continuum Limit," Springer Books, in: Sylvie Benzoni-Gavage & Denis Serre (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 145-159, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75712-2_12
    DOI: 10.1007/978-3-540-75712-2_12
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