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Griffith, J.S. (1968) Mathematics of Cellular Control Processes I. Negative Feedback to One Gene. Journal of Theoretical Biology, 20, 202-208.
http://dx.doi.org/10.1016/0022-5193(68)90189-6

has been cited by the following article:

  • TITLE: Global Stability in Dynamical Systems with Multiple Feedback Mechanisms

    AUTHORS: Morten Andersen, Frank Vinther, Johnny T. Ottesen

    KEYWORDS: Odes, Multiple Feedbacks, Stability, Global Stability, Attracting Trapping Region, Nonlinear Dynamics

    JOURNAL NAME: Advances in Pure Mathematics, Vol.6 No.5, April 26, 2016

    ABSTRACT: A class of n-dimensional ODEs with up to n feedbacks from the n’th variable is analysed. The feedbacks are represented by non-specific, bounded, non-negative C1 functions. The main result is the formulation and proof of an easily applicable criterion for existence of a globally stable fixed point of the system. The proof relies on the contraction mapping theorem. Applications of this type of systems are numerous in biology, e.g., models of the hypothalamic-pituitary-adrenal axis and testosterone secretion. Some results important for modelling are: 1) Existence of an attractive trapping region. This is a bounded set with non-negative elements where solutions cannot escape. All solutions are shown to converge to a “minimal” trapping region. 2) At least one fixed point exists. 3) Sufficient criteria for a unique fixed point are formulated. One case where this is fulfilled is when the feedbacks are negative.