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Bifurcation Behaviors Analysis on a Predator–Prey Model with Nonlinear Diffusion and Delay

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Abstract

In this paper, a class of predator–prey model with nonlinear diffusion and time delay is considered. The stability is investigated and Hopf bifurcation is demonstrated. Applying the normal form theory and the center manifold argument, we derive the explicit formulas for determining the properties of the bifurcating periodic solutions. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, main conclusions are included.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (no. 11261010), Soft Science and Technology Program of Guizhou Province (no. 2011LKC2030), Natural Science and Technology Foundation of Guizhou Province (J[2012]2100), Governor Foundation of Guizhou Province ([2012]53), Natural Science and Technology Foundation of Guizhou Province (2013) and Doctoral Foundation of Guizhou University of Finance and Economics (2010).

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Authors and Affiliations

  1. Guizhou Key Laboratory of Economics System Simulation, Guizhou Universityof Finance and Economics, Guiyang, People’s Republic of China

    Changjin Xu

  2. Department of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, People’s Republic of China

    Peiluan Li

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  1. Changjin Xu
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  2. Peiluan Li
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Correspondence to Changjin Xu.

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Xu, C., Li, P. Bifurcation Behaviors Analysis on a Predator–Prey Model with Nonlinear Diffusion and Delay. J Dyn Control Syst 20, 105–122 (2014). https://doi.org/10.1007/s10883-013-9208-1

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  • DOI: https://doi.org/10.1007/s10883-013-9208-1

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