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Geometric properties of a class of piecewise affine biological network models

Farcot, Etienne

Journal of mathematical biology, March 2006, Vol.52(3), pp.373-418 [Tạp chí có phản biện]

ISSN: 0303-6812 ; PMID: 16382313 Version:1

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  • Nhan đề:
    Geometric properties of a class of piecewise affine biological network models
  • Tác giả: Farcot, Etienne
  • Chủ đề: Models, Biological ; Eukaryotic Cells -- Cytology ; Prokaryotic Cells -- Cytology
  • Là 1 phần của: Journal of mathematical biology, March 2006, Vol.52(3), pp.373-418
  • Mô tả: The purpose of this report is to investigate some dynamical properties common to several biological systems. A model is chosen, which consists of a system of piecewise affine differential equations. Such a model has been previously studied in the context of gene regulation and neural networks, as well as biochemical kinetics. Unlike most of these studies, nonuniform decay rates and several thresholds per variable are assumed, thus considering a more realistic model. This model is investigated with the aid of a geometric formalism. We first provide an analysis of a continuous-space, discrete-time dynamical system equivalent to the initial one, by the way of a transition map. This is similar to former studies. Especially, the analysis of periodic trajectories is carried out in the case of multiple thresholds, thus extending previous results, which all concerned the restricted case of binary systems. The piecewise affine structure of such models is then used to provide a partition of the phase...
  • Ngôn ngữ: English
  • Số nhận dạng: ISSN: 0303-6812 ; PMID: 16382313 Version:1

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