Abstract
The variations of population size with respect to time are often described by means of differential equations. This paper assumes the population size follows an uncertain logistic population equation, and calculates its uncertainty distribution and α-paths. The first hitting time that the population size reaches a pre-set level is investigated, which forms an uncertain renewal process, based on which a harvesting strategy is designed. With the help of fundamental theorem of uncertain renewal processes, the optimal harvesting strategy problem is transformed to a traditional optimization problem involving two variables which could be easily solved analytically or numerically.
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