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Bifurcation analysis in a Holling-Tanner predator-prey model with strong Allee effect
- Source :
- Mathematical Biosciences and Engineering, Vol 20, Iss 5, Pp 8632-8665 (2023)
- Publication Year :
- 2023
- Publisher :
- AIMS Press, 2023.
-
Abstract
- In this paper, we analyze the bifurcation of a Holling-Tanner predator-prey model with strong Allee effect. We confirm that the degenerate equilibrium of system can be a cusp of codimension 2 or 3. As the values of parameters vary, we show that some bifurcations will appear in system. By calculating the Lyapunov number, the system undergoes a subcritical Hopf bifurcation, supercritical Hopf bifurcation or degenerate Hopf bifurcation. We show that there exists bistable phenomena and two limit cycles. By verifying the transversality condition, we also prove that the system undergoes a Bogdanov-Takens bifurcation of codimension 2 or 3. The main conclusions of this paper complement and improve the previous paper [30]. Moreover, numerical simulations are given to verify the theoretical results.
Details
- Language :
- English
- ISSN :
- 15510018 and 79568408
- Volume :
- 20
- Issue :
- 5
- Database :
- Directory of Open Access Journals
- Journal :
- Mathematical Biosciences and Engineering
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.9bb63525b5341afb066d2d795684088
- Document Type :
- article
- Full Text :
- https://doi.org/10.3934/mbe.2023379?viewType=HTML