Equilibria and Bogdanov-Takens Bifurcation Analysis in the Bazykin’s Predator-Prey System

Shuangte Wang, Hengguo Yu and Chunrui Zhang

Discrete Dynamics in Nature and Society, 2022, vol. 2022, 1-30

Abstract: In the paper, we proposed a Bazykin’s predator-prey system to explore the equilibrium point and Bogdanov-Takens bifurcation problems. Firstly, we derived some key parameter threshold conditions to ensure that the Bazykin’s predator-prey system had a multiple focus of multiplicity one, weak focus of order 2, cusps of codimension 2 and a degenerate Bogdanov-Takens singularity (focus or center case) of codimension 3. Furthermore, the distinction of two types of codimension 2 cusps was also discussed, which showed that the threshold of the two types of cusps could exhibit a cusp, which was a special case of the mentioned degenerate Bogdanov-Takens singularity (focus or center case) of codimension 3. Secondly, we systematically calculated that the Bazykin’s predator-prey system could undergo two types of Bogdanov-Takens bifurcations of codimension 2 and a degenerate focus type Bogdanov-Takens bifurcation of codimension 3. Finally, some numerical examples were implemented to verify the correctness and feasibility of mathematical theory derivation, which also directly showed all possible equilibrium points and Bogdanov-Takens bifurcations of Bazykin’s predator-prey system. In a word, all the research results could play an important theoretical support role in the study of controlling cyanobacteria bloom.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/ddns/2022/4844228.pdf (application/pdf)
http://downloads.hindawi.com/journals/ddns/2022/4844228.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:4844228

DOI: 10.1155/2022/4844228

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().