Key words and phrases: Lotka-Volterra model of 3-species, nonexistence of closed orbits, existence of nonconstant analytic rst integral, application of vector analysis, generalized May-Leonard model.

We will apply the successive approximation method forproving the Hyers--Ulam stability of a linear integral equation ofthe second kind.

we will apply the successive approximation method forproving the hyers--ulam stability of a linear integral equation ofthe second kind.

This article aims at preferring a new and viable algorithm, specifically a two-step homotopy perturbation transform algorithm (TSHPTA). This novel technique is a feasible way in finding exact solutions with a small amount of calculations. As a simple but typical example, it demonstrates the strength and the great potential of the two-step homotopy perturbation transform method to solve nonlinea...