Abstract
In this paper we study the cyclic gene model with repression considered by H. T. Banks and J. M. Mahaffy. Roughly, the model describes a biochemical feedback loop consisting of an integer number G of single gene reaction sequences in series. The model leads to a system of functional differential equations. We show that there is a qualitative difference in the dynamics between even and odd G if the feedback repression is sufficiently large. For even G, multiple stable steady states can coexist while for odd G, periodic orbits exist.
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This research was supported in part by the Air Force Office of Scientific Research under Contract #AFOSR-84-0376 and by the US Army Research Office under Contract #DAAG29-84-K-0082
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Smith, H. Oscillations and multiple steady states in a cyclic gene model with repression. J. Math. Biology 25, 169–190 (1987). https://doi.org/10.1007/BF00276388
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DOI: https://doi.org/10.1007/BF00276388