Asymptotic Behaviour Near a Nonlinear Sink

Details Asymptotic Behaviour Near a Nonlinear Sink Asymptotic Behaviour Near a Nonlinear Sink

2010-01-28

arxiv.org/abs/1001.5089v2

Mathematics

Classical Analysis and ODEs

31 pages, 1 figure, condensed or removed some sections and expanded others

Scientific paper

In this paper, we will develop an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This procedure is indifferent to resonance in the eigenvalues. Moreover, we will address the writing of one component of a solution in terms of the other in the case of a planar system. Examples will be given, notably the Michaelis-Menten mechanism of enzyme kinetics.

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