Stability and global Hopf bifurcation in a Leslie–Gower predator-prey model with stage structure for prey
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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.
KeywordsGlobal Hopf bifurcation Leslie–Gower Stage structure Predator-prey
Mathematics Subject Classification34D20 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).
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Conflict of interest
All authors declares that they have no conflict of interest.
- 9.Hale, J.K.: Theory of Functional Differerntial Equations. Springer, New York (1997)Google Scholar
- 16.Kuang, Y.: Delay Differerntial Equations with Application in Population Dynamics. Academic Press, Boston (1993)Google Scholar
- 18.Liu, C., Zhang, Q.L.: Dynamical behavior and stability analysis in a stage-structured prey predator model with discrete delay and distributed delay. Abstr Appl Anal 2014, Article ID 184174 (2014)Google Scholar
- 25.Meng, X.Y., Wu, Y.Q.: Bifurcation and control in a singular phytoplankton-zooplankton-fish model with nonlinear fish harvesting and taxation. Int. J. Bifur. Chaos. 28(3), 1850042 (2018)Google Scholar
- 29.Shaikh, A.A., Das, H., Ali, N.: Study of LG-Holling type III predator-prey model with disease in predator. J Appl Math Comput (2017). https://doi.org/10.1007/s12190-017-1142-z