Hopf bifurcation and optimal control in a diffusive predator-prey system with time delay and prey harvesting
Articles
Xiaoyuan Chang
Harbin Institute of Technology; Harbin University of Science and Technology, China
Junjie Wei
Harbin Institute of Technology, China
Published 2012-10-25
https://doi.org/10.15388/NA.17.4.14046
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Keywords

Hopf bifurcation
predator-prey system
harvesting
delay
optimal control.

How to Cite

Chang, X. and Wei, J. (2012) “Hopf bifurcation and optimal control in a diffusive predator-prey system with time delay and prey harvesting”, Nonlinear Analysis: Modelling and Control, 17(4), pp. 379–409. doi:10.15388/NA.17.4.14046.

Abstract

In this paper, we investigated the dynamics of a diffusive delayed predator-prey system with Holling type II functional response and nozero constant prey harvesting on no-flux boundary condition. At first, we obtain the existence and the stability of the equilibria by analyzing the distribution of the roots of associated characteristic equation. Using the time delay as the bifurcation parameter and the harvesting term as the control parameter, we get the existence and the stability of Hopf bifurcation at the positive constant steady state. Applying the normal form theory and the center manifold argument for partial functional differential equations, we derive an explicit formula for determining the direction and the stability of Hopf bifurcation. Finally, an optimal control problem has been considered.

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