Laboratory of Animal Feed Science, Division of Animal Science, Department of Animal and Marine Bioresource Sciences, Faculty of Agriculture, Kyushu University
九州大学大学院農学研究院動物資源科学部門家畜生産学講座飼料学研究室
This study was conducted to investigate dynamics of Lotka-Volterra equation by introducing the second derivative for change acceleration in the number of predators and prey. Lotka-Volterra equation gives a simple model to the analysis of predator-prey relationships. The results obtained were as follows. Introducing the second derivative into Lotka-Volterra equation gave the square of change rate of the number of predators and that of prey. Since the square of change rate gave positive value, the following two inequalities were given. (1) Change acceleration of the number of prey per prey was higher than the product of -$ \beta $ and change rate of the number of predators. (2) Change acceleration of the number of predators per predator was higher than the product of $ delta $ and change rate of the number of prey. These two might be related to the change in the number of predators and prey. It was suggested from the present study that investigating dynamics of Lotka-Volterra equation gave inequalities showing some change aspects of predator-prey relationships.
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