The Period in the Volterra–Lotka Predator-Prey Model

The Volterra–Lotka predator-prey differential equations ${{dX} / {dt}} = aX(Y - 1),{{dY} / {dt}} = - bY(x - 1)$ possess a one-parameter family of periodic solutions. The period P of these solutions is investigated. By means of a suitable transformation P is represented as the integral over a full period of an easily computable real-analytic periodic function. Hence the trapezoidal rule provides an efficient algorithm for the numerical calculation of P. Furthermore, an asymptotic expansion for large values of P is derived by means of inverse Laplace asymptotics.