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Optimal Harvest Control in a Singular Prey-Predator Fishery Model with Maturation Delay and Gestation Delay

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  • Chao Liu
  • Longfei Yu
  • Qingling Zhang

Abstract

This paper presents a singular prey-predator fishery model, where maturation delay for prey and gestation delay for predator are considered. Fishing efforts are introduced to harvest prey and predator population, which are developed as control instruments to investigate optimal utilization of fishery resource. By analyzing associated characteristic equation, local stability analysis is studied due to combined variations of double time delays. Furthermore, Pontryagin’s maximum principle is utilized to characterize optimal harvest control, and the optimality system is numerically solved based on an iterative method.

Suggested Citation

  • Chao Liu & Longfei Yu & Qingling Zhang, 2016. "Optimal Harvest Control in a Singular Prey-Predator Fishery Model with Maturation Delay and Gestation Delay," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-9, November.
    • Handle: RePEc:hin:jnddns:4398527
    DOI: 10.1155/2016/4398527
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