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Global analysis in Bazykin's model with Holling II functional response and predator competition.
- Source :
-
Journal of Differential Equations . Apr2021, Vol. 280, p99-138. 40p. - Publication Year :
- 2021
-
Abstract
- In this paper, we study the well-known Bazykin's model with Holling II functional response and predator competition. A detailed bifurcation analysis, depending on all four parameters, reveals a rich bifurcation structure, including supercritical and subcritical Bogdanov-Takens bifurcation, degenerate Hopf bifurcation of codimension at most 2, and a focus type degenerate Bogdanov-Takens bifurcation of codimension 3, originating from a nilpotent focus of codimension 3 which acts as the organizing center for the bifurcation set. Moreover, some sufficient conditions to guarantee the global asymptotical stability of the semi-trivial equilibrium or the unique positive equilibrium are also given. Our analysis indicates that we can classify the long-time dynamics of the model with a threshold value c 0 for the natural mortality rate c of predators, in detail, the following are true. (i) When c ≥ c 0 , the prey will persist and predators will eventually go extinct for all positive initial populations. (ii) When c < c 0 , the prey and predators will coexist, for all positive initial populations, in the form of multiple positive equilibria or multiple periodic orbits. Our results can be seen as a complement to the work by Bazykin et al. [2–5] , Hainzl [22,23] , Kuznetsov [30]. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 280
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 148773900
- Full Text :
- https://doi.org/10.1016/j.jde.2021.01.025