Analysis of the Picard's Iteration Method and Stability for Ecological Initial Value Problems of Single Species Models with Harvesting Factor

Abstract

In the recent decades, biology and ecology area and also computer and network sciences are marched on at a rapid pace toward perfection by help of mathematical concepts such as stability, bifurcation, chaos and etc.  Because of no existing any interspecific interaction in the single species, one is able to see that this is the simplest model. Meanwhile by adding some assumptions, we see that it has so many practical applications in the nature and any branch of sciences. In this article, some dynamical models of single species are studied. First, Picard's iteration method for exponential growth rate is analyzed. In continuation, some logistic models for both cases without harvesting and having harvested factor which are constant or variable are studied. Indeed, the solution and stability of equilibria for the said models are analyzed. Finally, in the section of simulation analysis by help of \textit{mathlab software}, we give some numerical simulations to support of our mathematical conclusions which show the stability of the equilibria for I.V.Ps. of the logistic equation developed.