Dynamical behavior in a stage-structured differential-algebraic prey-predator model with discrete time delay and harvesting

Authors:
Chao Liu;Qingling Zhang;Xue Zhang;Xiaodong Duan
Affiliations:
Department of Information and Computational Science, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, PR China and Institute of Systems Science, Northeastern University, Shenyang, 1100 ...;Institute of Systems Science, Northeastern University, Shenyang, 110004, PR China and Key Laboratory of Integrated Automation of Process Industry, Ministry of Education, Northeastern University, S ...;Institute of Systems Science, Northeastern University, Shenyang, 110004, PR China and Key Laboratory of Integrated Automation of Process Industry, Ministry of Education, Northeastern University, S ...;Institute of Nonlinear Information Technology, Dalian Nationalities University, Dalian, 116600, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 3
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Abstract

A differential-algebraic model system which considers a prey-predator system with stage structure for prey and harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, dynamic behavior of the proposed model system with and without discrete time delay is investigated. Local stability analysis of the model system without discrete time delay reveals that there is a phenomenon of singularity induced bifurcation due to variation of the economic interest of harvesting, and a state feedback controller is designed to stabilize the proposed model system at the interior equilibrium; Furthermore, local stability of the model system with discrete time delay is studied. It reveals that the discrete time delay has a destabilizing effect in the population dynamics, and a phenomenon of Hopf bifurcation occurs as the discrete time delay increases through a certain threshold. Finally, numerical simulations are carried out to show the consistency with theoretical analysis obtained in this paper.