1976 年 26 巻 4 号 p. 191-197
A simple mathematical model originating from Shinozaki's predator-prey model is proposed to simulate the one-producer-one-consumer system. To construct the model the following assumptions are made : the producer-biomass follows the exponential growth curve and the rate of its loss is proportional to the consumer-biomass, while the consumer-biomass follows an logistic crrve whose asymptote is proportional to the producer-biomass. The exact analytical solutions of the present non-linear model distinguish between various patterns of growth curves of producer-and consumer-biomasses. Properties of growth curves, such as extreme values of biomass, extinction time, biomass duration, etc. are discussed from both biological and mathematical viewpoints.