Abstract
In the classical prey-predator system of Lotka-Volterra, the period of each solution depends on the value of the first integral, which is sometimes called energy. The period is to be asymptotically expressed with the energy when it is very large (Theorem 13 in §3). In addition, the time average of umvn (u, v: the unknowns of the Lotka-Volterra system) will be estimated in §4.
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References
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Oshime, Y. Asymptotic expression of the period of the Lotka-Volterra system. Japan J. Indust. Appl. Math. 20, 353–378 (2003). https://doi.org/10.1007/BF03167427
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DOI: https://doi.org/10.1007/BF03167427