Stability and global Hopf bifurcation in a Leslie–Gower predator-prey model with stage structure for prey

  • Xin-You MengEmail author
  • Hai-Feng Huo
  • Xiao-Bing Zhang
Original Research


This paper is concerned with a predator-prey model with Leslie–Gower functional response and stage structure for prey. By regarding time delay as the bifurcation parameter, sufficient conditions for the local stability of the positive equilibrium and the existence of Hopf bifurcation are given. Some explicit formulas determining the properties of Hopf bifurcation are established by using the normal form method and center manifold theorem. The global continuation of periodic solutions bifurcating from the positive equilibrium is given due to a global Hopf bifurcation result for functional differential equations. Finally, numerical simulations are carried out to show consistency with theoretical analysis.


Global Hopf bifurcation Leslie–Gower Stage structure Predator-prey 

Mathematics Subject Classification

34D20 92D25 93D20 37N25 



The authors convey their sincere thanks and gratitude to four reviewers for their suggestions towards the improvement of the manuscript. This work is supported by the National Natural Science Foundation of China (Grant Nos. 1661050 and 11461041), and the Development Program for HongLiu Outstanding Young Teachers in Lanzhou University of Technology (Q201308).

Compliance with ethical standards

Conflict of interest

All authors declares that they have no conflict of interest.


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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.School of ScienceLanzhou University of TechnologyLanzhouChina

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