# Asymptotic Behaviour Near a Nonlinear Sink

Source: [Asymptotic Behaviour Near a Nonlinear Sink](<https://www.sota2.com/research/paper/68fa4f371e209131ce961d69>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:12:48.492Z

Authors: Matt S. Calder, David Siegel

Published: 2010-01-28T07:20:23.000Z

## Abstract

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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1001.5089>)

[PDF](<https://arxiv.org/pdf/1001.5089.pdf>)