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Bifurcation analysis in a modified Lesile–Gower model with Holling type II functional response and delay

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Abstract

In this paper, a modified Lesile–Gower predator–prey system with delay is considered. The existence of Hopf bifurcations at the positive equilibrium is established by analyzing the distribution of the characteristic values. Furthermore, different to previous papers, a multiple time scale technique is employed to calculate the normal form on the center manifold of delay differential equations, which is much easier to implement in practice than the conventional method, center manifold reduction. Finally, to verify our theoretical predictions, some numerical simulations are also included.

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Acknowledgments

We would like to thank the reviewers for their valuable comments and suggestions on the manuscript. This work was supported by the National Natural Science Foundation of China (No: 11371058 and 11501159) and the Youth Foundation of Hebei University (No: 2014-295).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Hebei University, Baoding, 071002, China

    Jianzhi Cao

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Rong Yuan

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  1. Jianzhi Cao
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  2. Rong Yuan
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Correspondence to Jianzhi Cao.

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Cao, J., Yuan, R. Bifurcation analysis in a modified Lesile–Gower model with Holling type II functional response and delay. Nonlinear Dyn 84, 1341–1352 (2016). https://doi.org/10.1007/s11071-015-2572-5

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  • DOI: https://doi.org/10.1007/s11071-015-2572-5

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