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Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation
Applied and Computational Mathematics
Volume 4, Issue 1, February 2015, Pages: 20-29
Received: Nov. 14, 2014; Accepted: Nov. 29, 2014; Published: Feb. 2, 2015
Authors
Rui-Ling Zhang, College of Resources and Environmental Science, Gansu Agricultural University, Gansu 730070, PR China
Wan-Xiong Wang, College of Resources and Environmental Science, Gansu Agricultural University, Gansu 730070, PR China
Li-Juan Qin, College of Resources and Environmental Science, Gansu Agricultural University, Gansu 730070, PR China
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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.
Keywords
Discrete-Time Predator-Prey Model, Equilibrium, Pontryagin Maximum Principle, Bifurcation, Sustainable Development
Rui-Ling Zhang, Wan-Xiong Wang, Li-Juan Qin, Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation, Applied and Computational Mathematics. Vol. 4, No. 1, 2015, pp. 20-29. doi: 10.11648/j.acm.20150401.14
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