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

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.