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DYNAMIC ANALYSIS IN A HARVESTED DIFFERENTIAL-ALGEBRAIC PREY–PREDATOR MODEL

Department of Information and Computational Science, Northeastern University of Qinhuangdao, Qinhuangdao 066004, P.R. China

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QINGLING ZHANG

Institute of Systems Science, Key Laboratory of Integrated Automation of Process Industry, Ministry of Education, Northeastern University, Shenyang Liaoning 110004, China

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, and

XUE ZHANG

Institute of Systems Science, Key Laboratory of Integrated Automation of Process Industry, Ministry of Education, Northeastern University, Shenyang Liaoning 110004, China

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https://doi.org/10.1142/S0219519409002833Cited by:7 (Source: Crossref)

Abstract

Nowadays, the biological resource in the prey–predator ecosystem is commercially harvested and sold with the aim of achieving economic interest. Furthermore, the harvest effort is usually influenced by the variation of economic interest of harvesting. In this paper, a differential–algebraic model is proposed, which is utilized to investigate the dynamical behavior of the prey–predator ecosystem due to the variation of economic interest of harvesting. By discussing the local stability of the proposed model around the interior equilibrium, the instability mechanism of harvested prey–predator ecosystem is studied. With the purpose of stabilizing the proposed model around the interior equilibrium and maintaining the economic interest of harvesting at an ideal level, a feedback controller is designed. Finally, numerical simulations are carried out to demonstrate consistency with the theoretical analysis.

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