Analytical approximations and Padé approximants for Volterra's population model

摘要

In this paper, an analytic approximation for Volterra's model for population growth of a species in a closed system is presented. The nonlinear integro-differential model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation. The series solution method and the decomposition method are implemented independently to the model and to a related ODE. The Padé approximants, that often show superior performance over series approximations, are effectively used in the analysis to capture the essential behavior of the population u(t) of identical individuals.