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A generalized predator–prey system with multiple discrete delays and habitat complexity

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Abstract

A generalized predator–prey model with multiple discrete delays and the effect of habitat complexity is proposed in this paper. Firstly, the stability of the considered model system and existence of Hopf bifurcations are investigated by the differential equation theory. Secondly, the direction of Hopf bifurcations and the stability of bifurcating periodic solutions are determined by applying the normal form theory and the center manifold reduction for functional differential equations. Most importantly and interestingly, this paper gives a class of the corresponding model systems, and some published works become special cases of ours.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (no. 11301238) and the Fundamental Research Funds for the Central Universities (no. lzujbky-2017-166).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People’s Republic of China

    Zhihui Ma

  2. School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou, 730000, Gansu, People’s Republic of China

    Shufan Wang

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  1. Zhihui Ma
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  2. Shufan Wang
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Correspondence to Zhihui Ma.

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Ma, Z., Wang, S. A generalized predator–prey system with multiple discrete delays and habitat complexity. Japan J. Indust. Appl. Math. 36, 385–406 (2019). https://doi.org/10.1007/s13160-019-00343-9

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  • DOI: https://doi.org/10.1007/s13160-019-00343-9

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