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Some modified Michaelis–Menten equations having stable closed trajectories

Published online by Cambridge University Press:  14 November 2011

Russell A. Smith
Russell A. Smith
Affiliation:
Department of Mathematical Sciences, Science Laboratories, The University, South Road, Durham DH1 3LE, U.K.
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Abstract

A 3-dimensional autonomous ordinary differential equation is studied which models certain cellular biochemical reactions. Extended Poincaré-Bendixson theory is used to obtain algebraic conditions on the parameters which are sufficient for the existence of at least one stable closed trajectory. Similar conditions are also obtained for the absence of chaos and for the global convergence of solutions to a critical point.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 109 , Issue 3-4 , 1988 , pp. 341 - 359
Copyright
Copyright © Royal Society of Edinburgh 1988

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