Volume 42 Issue 5
May  2021
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LIU Rong, LIU Guirong. Optimal Harvesting in a Periodic 3-Species Predator-Prey Model With Size Structure in Predators[J]. Applied Mathematics and Mechanics, 2021, 42(5): 510-521. doi: 10.21656/1000-0887.410285
 Citation: LIU Rong, LIU Guirong. Optimal Harvesting in a Periodic 3-Species Predator-Prey Model With Size Structure in Predators[J]. Applied Mathematics and Mechanics, 2021, 42(5): 510-521.

# Optimal Harvesting in a Periodic 3-Species Predator-Prey Model With Size Structure in Predators

##### doi: 10.21656/1000-0887.410285
Funds:  The National Natural Science Foundation of China（12001341；11971279）
• Rev Recd Date: 2021-03-12
• Publish Date: 2021-05-01
• The research on population dynamics and related control problems is not only of theoretical significance, but also closely related to biodiversity protection, pest control, and the development and utilization of renewable resources. The optimal harvesting problem was considered in a periodic 3-species predator-prey system with 1 predator and 2 competing preys, where the predator has size structure and was described with 1st-order partial differential equations. First, the existence of a unique non-negative solution of the controlled system was proven by means of the fixed-point reasoning, and the continuous dependence of the solution on the control variables was discussed. Then, the optimal harvesting conditions were given with the techniques of tangential-normal cones and the adjoint system. Finally, with Ekeland’s variational principle, the existence of the optimal harvesting strategy was derived. Here the objective functional represents the net economic benefit in the harvesting of 3 species. The results obtained would be beneficial for exploration of renewable resources.
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