Approximate Analytical Solution of the Nonlinear System of Differential Equations Having Asymptotically Stable Equilibrium

Abstract

The present paper is concerned with the purely analytic solutions of the
highly nonlinear systems of differential equations possessing an asymptotically
stable equilibrium. A methodology combined with the homotopy
analysis method is proposed. The methodology involves proper introduction
of an auxiliary linear operator and an auxiliary function during the
implementation of the homotopy method so that it can yield uniformly
valid solutions, not affected from the existing parameters or initial conditions.
The technique is applied to the systems particularly appearing
in mathematical biology. The obtained explicit analytical expressions for
the solution generate results that compare excellently with the numerically
computed ones.