The classical Lotka-Volterra System of two ordinary differential equations (one prey-one predator) is considered. It is well known that this system has a first integral and that every non-constant solution of this system is periodic. However, the precise estimate of the period of the solution with respect to the value of the first integral has not been well known yet. The first topic of the present paper is a detailed answer to this question. The second topic is the monotone dependence of the period on the value of the first integral.
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