Affiliations: Department of Applied Mathematics, University of Western Ontario, London, ON, Canada. E-mail: mcalder9@uwo.ca | Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada. E-mail: dsiegel@math.uwaterloo.ca
Note: [] Corresponding author: Matt S. Calder, Department of Applied Mathematics, University of Western Ontario, 1151 Richmond Street, London, ON, Canada N6A 5B7. Tel.: +1 519 661 2111 X88787; Fax: +1 519 661 3523; E-mail: mcalder9@uwo.ca.
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.
