Skip to content
DraconiticResearch
Search Sources API
197,785 studies31 sourcesUpdated 45 min ago
Peer-reviewedCC BY 4.0Mathematics

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

  • Chaoliang Luo1
  • Zhiyi Tan1
  • Shunlian Liu1
  • Yulin Zhao1
  1. 1College of Science, Hunan University of Technology, Zhuzhou 412007, China
Open at sourceDOICite

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.

Related

  1. Spatial Dynamics in a Diffusive Leslie–Gower Predator–Prey Model with Allee Effect, Harvesting, and Cooperative Hunting
    Na Min, Hongyang Zhang, Shengkun Xie
    MathematicsPeer-reviewedCC BY 4.0Epidemiology & public healthCrossref
  2. A Minimal Stochastic Model of Microbial Ecological Dynamics in a Single-Species-Single-Resource Setting.
    Cheuk Fung Alvin Leung, Anatoly B Kolomeisky
    The journal of physical chemistry. BPeer-reviewedCC BY-NC-NDFull text1 citedEpidemiology & public healthEurope PMC
  3. Spatiotemporal dynamics in a diffusive Leslie–Gower model: Turing instability and bifurcations with prey Allee effect and predator fear effect
    Ye Han, Wanqin Wu, Xuewen Tan +2
    Infectious Disease ModellingPeer-reviewedCC BYFull textEpidemiology & public healthDOAJ
  4. Endoscopic versus open vein harvesting technique and 2-year saphenous vein graft patency: A subanalysis of the Newton-CABG CardioLink-5 randomized trial.
    Raj Verma, Hwee Teoh, Lawrence A Leiter +12
    JTCVS openPeer-reviewedCC BY-NC-NDFull textSurgery & anaesthesiaEurope PMCPMC
  5. Artificial light at night suppresses the metabolic response of a coral reef fish to a virtual predator
    Izzy C Tiddy, Manuel Vidal, Suzanne C Mills +2
    Conservation PhysiologyPeer-reviewedCC BY 4.0Full textEcologyZoology & animal behaviourHAL

Cite

BibTeXRIS
BibTeX
@article{luo2026optimal,
  title = {{Optimal Harvesting of a Stochastic Three-Species Predator–Prey Model with Multiplicative Noise}},
  author = {Chaoliang Luo and Zhiyi Tan and Shunlian Liu and Yulin Zhao},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203675},
  url = {https://www.mdpi.com/2227-7390/14/20/3675},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Optimal Harvesting of a Stochastic Three-Species Predator–Prey Model with Multiplicative Noise
AU  - Chaoliang Luo
AU  - Zhiyi Tan
AU  - Shunlian Liu
AU  - Yulin Zhao
PY  - 2026
DA  - 2026/10/10
JO  - Mathematics
DO  - 10.3390/math14203675
UR  - https://www.mdpi.com/2227-7390/14/20/3675
AB  - 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.
SN  - 2227-7390
ER  -