Structure-Preserving Simulation of the Lotka-Volterra System

The Lotka-Volterra system is traditionally integrated with the classical Runge-Kutta method of order four or the Runge-Kutta-Fehlberg method which fails to preserve the special structure of the system in long term integration. This paper transforms the Lotka-Volterra system into a Hamiltonian system and integrates it with two highly efficient symplectic methods. The results of the numerical simulation show the robustness of these methods.