Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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BIFURCATION ANALYSIS OF A DELAYED PREDATOR-PREY MODEL OF PREY MIGRATION AND PREDATOR SWITCHING

  • Xu, Changjin (Guizhou Key Laboratory of Economics System Simulation School of Mathematics and Statistics Guizhou University of Finance and Economics / School of Mathematical Science and Computing Technology Central South University) ;
  • Tang, Xianhua (School of Mathematical Science and Computing Technology Central South University) ;
  • Liao, Maoxin (School of Mathematical Science and Computing Technology Central South University)
  • Received : 2009.11.08
  • Published : 2013.03.31
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Abstract

In this paper, a class of delayed predator-prey models of prey migration and predator switching is considered. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given.

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References

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