Series solution of the multispecies Lotka-Volterra equations by means of the homotopy analysis method

Abstract

The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopyanalysis method (HAM). The continuous solution for the nonlinear system is given, whichprovides a convenient and straightforward approach to calculate the dynamics of the system.The HAM continuous solution generated by polynomial base functions is of comparable accuracyto the purely numerical fourth-order Runge-Kutta method. The convergence theorem forthe three-dimensional case is also given.