Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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A Hopf bifurcation in single-loop positive-feedback systems


Author: James F. Selgrade
Journal: Quart. Appl. Math. 40 (1982), 347-351
MSC: Primary 58F14; Secondary 34C15, 34C25, 92A09
DOI: https://doi.org/10.1090/qam/678206
MathSciNet review: 678206
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Abstract: This paper gives sufficient conditions for a Hopf bifurcation in a five-dimensional system of ordinary differential equations which provides a model for positive feedback in biochemical control circuits. These conditions only depend on the feedback function and its first and second derivative. The conditions are used to exhibit Hopf bifurcations for the Griffith equations and the Tyson-Othmer equations.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/678206
Article copyright: © Copyright 1982 American Mathematical Society


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