Work

Optimal Harvesting of a Stochastic Three-Species Predator–Prey Model with Multiplicative Noise

Year: 2026

Type: article

Abstract: This paper addresses the optimal harvesting of a stochastic three-species predator–prey system with multiplicative noise and harvesting efforts. We first establish sufficient conditions for the persistence and extinction of each species and derive threshold-type criteria in terms of harvesting efforts. Under suitable competition coefficient conditions, we prove that the system is asymptotically stable in distribution. We then characterize the feasible harvesting region and, by applying the ergodic method, obtain the explicit optimal harvesting effort and the corresponding maximum expectation of sustainable yield when the feasibility condition holds; otherwise, we prove that no interior optimal harvesting strategy exists, show that any optimal strategy (if it exists) must lie on the boundary of the feasible region, and provide the corresponding necessary boundary KKT conditions. Numerical simulations validate the theoretical results and illustrate the effect of noise intensity on the existence of the optimal strategy and sustainable yield.

Source: Mathematics

DOI: 10.3390/math14203675

Authors: Chaoliang Luo, Zhiyi Tan, Shunlian Liu, Yulin Zhao

Institution: Hunan University of Technology

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: Education Department of Hunan Province, National Natural Science Foundation of China