Bulletin of Mathematical Biology

, Volume 49, Issue 3, pp 307–320 | Cite as

A nonlinear treatment of the protocell model by a boundary layer approximation

  • Kazuaki Tarumi
  • Helmut Schwegler


The “protocell” is a mathematical model of a self-maintaining unity based on the dynamics of simple reaction-diffusion processes and a self-controlled dynamics of the surface. In this paper its spatio-temporal behaviour far from the stationary structure is investigated by means of a boundary layer approximation. It is shown in detail how a simplified and mathematically feasible equation can be derived from the original parabolic problem. It turns out that the known instability which is initiated in the linear region around the stationary structure is continued further in the direction to a division by nonlinear dynamics.


Linear Stability Analysis Surface Motion Division Process Nonlinear Region Boundary Layer Approximation 
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Copyright information

© Society for Mathematical Biology 1987

Authors and Affiliations

  • Kazuaki Tarumi
    • 1
  • Helmut Schwegler
    • 1
  1. 1.Institute of Theoretical Physics and Center for Biosystems ResearchUniversity of BremenBremen 33F.R.G.

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