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Stability and Hopf bifurcation in a reaction–diffusion predator–prey system with interval biological parameters and stage structure

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Abstract

This paper deals with a delayed reaction–diffusion predator–prey system combined with stage structure for prey and interval biological parameters. By taking the sum of delays as the bifurcation parameter, the local stability of the equilibrium points is investigated and the condition of Hopf bifurcation is obtained. In succession, using the normal form theory and the center manifold reduction for partial functional differential equations, we derive the explicit formulas determining stability, direction and other properties of bifurcating periodic solutions. Some numerical simulations are also included to illustrate our theoretical results.

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Acknowledgments

The authors would like to show sincere thanks to the anonymous reviewers for their valuable suggestions. The work is supported by National Natural Science Foundation of China under Grant 61174155 and Grant 11032009. The work is also sponsored by Qing Lan Project of Jiangsu and Funding of Jiangsu Innovation Program for Graduate Education KYZZ_0088, the Fundamental Research Funds for the Central Universities.

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  1. Department of Mathematics, School of Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Hongyong Zhao & Ling Wang

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  1. Hongyong Zhao
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  2. Ling Wang
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Correspondence to Hongyong Zhao.

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Zhao, H., Wang, L. Stability and Hopf bifurcation in a reaction–diffusion predator–prey system with interval biological parameters and stage structure. Nonlinear Dyn 79, 1797–1816 (2015). https://doi.org/10.1007/s11071-014-1775-5

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  • DOI: https://doi.org/10.1007/s11071-014-1775-5

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