A Hopf bifurcation in single-loop positive-feedback systems
- 1 January 1982
- journal article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 40 (3) , 347-351
- https://doi.org/10.1090/qam/678206
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.Keywords
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