A Remark on the Period of the Periodic Solution in the Lotka - Volterra System

The Lotka-Volterra equations have been at the root of almost every investigation into population dynamics for the last few decades. They predict the existence of population cycles in which the period is an important parameter. It is well known that (1.1) has a one-parameter family of periodic solutions with the equilibrium (y/S, a//3) as center point. Volterra 131 computed that for small disturbance of the equilibrium the period of such a solution is T=: 271/G., Grasman and Veling [2] gave an asymptotic formula for the period which holds for large disturbances. Frame [ 11 expressed the period T as power series. In this paper, we express the period T