Periodic solution and control optimization of a prey-predator model with two types of harvesting

• Published in: Advances in difference equations Vol. 2018; no. 1; pp. 1 - 14
• Main Authors: Wang, Jianmei, Cheng, Huidong, Liu, Hongxia, Wang, Yanhui
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 25.01.2018; SpringerOpen
• Subjects: Analysis; Difference and Functional Equations; Functional Analysis; Mathematics; Mathematics and Statistics; optimization; order-1 periodic solution; Ordinary Differential Equations; Partial Differential Equations; prey-predator model; stability; state-dependent impulse; 34C25; prey-predator model; 34A37; 92B05; optimization; 34D20; state-dependent impulse; order-1 periodic solution; stability
• ISSN: 1687-1847; 1687-1847
• DOI: 10.1186/s13662-018-1499-9

In this work, a prey-predator model with both state-dependent impulsive harvesting and constant rate harvesting is investigated, where the replenishment rate of prey and the harvesting rate are linearly related with the selected threshold. By first using the successor function method and differential equation geometry theory, the existence, uniqueness and asymptotic stability of the order-1 periodic solution are discussed. And then numerical simulations with an example are given to illustrate the feasibility of the theorem-related results. Moreover, in order to increase the total profit, the optimization strategy is presented and the optimal threshold is obtained.