Competitive Predator-Prey Systems with Time-Dependent Coefficients: A Multistage Homotopy Perturbation Analysis

Abstract

This paper treats competitive predator-prey systems, which growth of populations and their mutual interactions are time dependent. For solving a general Lotka-Volterra system of equations, the multistage homotopy perturbation (MH-P) method  is developed to predict the time evolution of the dynamical system and its properties, such as existence of stable periodic orbits. As the newest achievement, the efficiency of MH-P method is provedintreatment of almost-periodic variations of coefficients with incommensurate excitation frequencies.The periodic variations of coefficients are analyzed as special case by assuming that excitation frequencies are commensurate. By using MH-P method, the approximate analytic solutions are obtained, which are very accurate in the long term behaviour. Although an usefull convergence test of the computed solution is provided, the accuracy of  MH-P method is compared also by results of the numerical integration of Lotka-Volterra equations by using the Runge-Kutta method, where an excellent agreement is obtained.