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Hopf Bifurcation of a Modified Leslie--Gower Predator--Prey System

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Abstract

In this paper, Hopf bifurcation is studied for a modified Leslie--Gower predator--prey system with harvesting. Our modified system is a biological economic cognitive system. An important feature of the biological economic cognitive system is that the harvest effort on the predator--prey system is investigated from an economic perspective. By using the local parameterization method and Hopf bifurcation theory, we obtain some new criteria for the Hopf bifurcation. Lastly, a numerical example is provided to demonstrate the effectiveness of our results.

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Acknowledgments

The authors are greatly indebted to the anonymous reviewers and the editor for their insightful comments. The work is supported by Key Science Foundation of Educational Department of Hubei Province under Grant D20082201.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Xinyu University, Xinyu, 338004, People’s Republic of China

    Wei Liu

  2. College of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, People’s Republic of China

    Chaojin Fu

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  1. Wei Liu
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  2. Chaojin Fu
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Correspondence to Wei Liu or Chaojin Fu.

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Liu, W., Fu, C. Hopf Bifurcation of a Modified Leslie--Gower Predator--Prey System. Cogn Comput 5, 40–47 (2013). https://doi.org/10.1007/s12559-012-9162-3

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  • DOI: https://doi.org/10.1007/s12559-012-9162-3

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