Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation

Abstract

This paper deals with a discrete-time prey-predator system with Holling type-IV function response in the presence of some alternative food to predator and harvesting of prey species. By theoretical analysis and numerical simulation, comparing with the system without harvesting, ecological equilibrium point of the system is removed if harvesting effort is changed, and the appropriate harvesting effort can increase the stability of the system. Moreover, optimal harvesting policy is obtained using Pontryagin's maximum principle. Meanwhile, some numerical simulations verify our analytical results. This study also gains the maximum economic profit which is based on the ecological equilibrium. The suitable price of resources can control the excessive harvest to promote the sustainable development of species.

Optimal control of linear time‐delay systems by a hybrid of block‐pulse functions and biorthogonal cubic Hermite spline multiwavelets

“…1 Therefore, finding the optimal solution for these systems is interesting to many researchers. [2][3][4][5][6][7][8][9][10] Although the optimal control problem for linear systems without delays was solved in the 1960s, 11 the optimal control problem for linear systems with delays is still open, depending on the delay type, specific system equation, criterion, etc. 12 Kharatishvili extended the Pontryagin maximum principle to time-delay systems and obtained conditions for optimality.…”