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Stability and Hopf bifurcation of a delayed-diffusive predator–prey model with hyperbolic mortality and nonlinear prey harvesting

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Abstract

In this paper, a delayed-diffusive predator–prey model with hyperbolic mortality and nonlinear prey harvesting subject to the homogeneous Neumann boundary conditions is investigated. Firstly, the global asymptotic stability of the unique positive constant equilibrium is obtained by an iteration technique. Secondly, regarding time delay as a bifurcation parameter and using the normal form theory and center manifold theorem, the existence, stability and direction of bifurcating periodic solutions are demonstrated, respectively. Finally, numerical simulations are conducted to illustrate the theoretical analysis.

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Acknowledgements

This work was supported by the Natural Science Foundation of Shandong Province of China (No. ZR2014AQ014), the Special Funds of the National Natural Science Foundation of China (No. 11426217), the NSFC (Nos. 11602305, 11501572, 11401586 and 11301333) and the Fundamental Research Funds for the Central Universities (Nos. 15CX05064A and 16CX02055A).

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  1. Department of Mathematics, China University of Petroleum, Qingdao, 266580, People’s Republic of China

    Fengrong Zhang & Yan Li

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  1. Fengrong Zhang
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Correspondence to Yan Li.

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Zhang, F., Li, Y. Stability and Hopf bifurcation of a delayed-diffusive predator–prey model with hyperbolic mortality and nonlinear prey harvesting. Nonlinear Dyn 88, 1397–1412 (2017). https://doi.org/10.1007/s11071-016-3318-8

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