Optimal pulse harvesting strategy based on uncertain Gompertz population model

Abstract Based on the basic principles of the renewal process and α-paths, uncertain Gompertz population equation and optimal pulse harvesting strategy of uncertain Gompertz population equation are proposed in this paper. It is a differential equation of uncertain population model driven by canonical Liu process. First of all, the solution of Gompertz population equation with uncertainty is proposed for the first time. Whereafter, the uncertainty distribution and α-paths are given. Based on the basic principles of the renewal process, we study the population number following the uncertain Gompertz population equation, calculate the first hitting time when it reaches the preset level, design an accurate harvesting strategy which could be transformed into an problem of the maximum value of two variables.