Bifurcation analysis in a predator-prey system with stage-structure and harvesting |
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| Authors: | Ying Qu Junjie Wei |
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| Institution: | a Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
b Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, Shandong 264209, China |
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| Abstract: | In this paper, we consider a predator-prey model with stage-structure and harvesting. This model is the same as the one developed by Kar and Pahari (2007) 9], but we make bifurcation analysis more general than their work. In particular, using the approach of Beretta and Kuang (2002) 4], we show that the positive steady state can be destabilized through a Hopf bifurcation. We also investigate the stability and direction of periodic solutions bifurcating from Hopf bifurcation by using the normal form theory and the center manifold theorem presented in Hassard et al. (1981) 8]. Numerical simulations are then carried out as supporting evidences of our analytical results. |
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| Keywords: | Predator-prey system Harvesting Time-delay Stability Hopf bifurcation |
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