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

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. 1 ( ) ( )/( 1 + ( ) ( )) + 2 ( ) ( )/( 2 + ( ) ( )), where 1 , 2 , 1 , 2 are all positive constants. Let represent cost of Hindawi Publishing Corporation

Stability and Bifurcation Analysis of a Discrete Singular Bioeconomic System

“…Liu et al [11] analyzed the local dynamics and Hopf bifurcation for a biological economic model with Holling type II functional response and harvesting effort on prey. Liu et al [12] proposed a singular fishery model for a class of prey-predator interaction with gestation delay for predator and maturation delay for prey. Liu et al [13] formulated and discussed a singular predatorprey model by implementing commercial harvesting on predator with gestation delay for predator and maturation delay for prey.…”