Bifurcation and Chaos of a Nonlinear Discrete-Time Predator-Prey Model Involving the Nonlinear Allee Effect

Ning Song and Marcio Eisencraft

Discrete Dynamics in Nature and Society, 2023, vol. 2023, 1-32

Abstract: The complex dynamics of a nonlinear discretized predator-prey model with the nonlinear Allee effect in prey and both populations are investigated. First, the rigorous results are derived from the existence and stability of the fixed points of the model. Second, we establish a model with the Allee effect in prey undergoing codimension-one bifurcations (flip bifurcation and Neimark–Sacker bifurcation) and codimension-two bifurcation associated with 1 : 2 strong resonance by using center manifold theorem and bifurcation theory, and the direction of bifurcations is also evaluated. In particular, chaos in the sense of Marotto is proved at some certain conditions. Third, numerical simulations are performed to illustrate the effectiveness of the theoretical results and other complex dynamical behaviors, such as the period-3, 4, 6, 8, 9, 30, and 43 orbits, attracting invariant cycles, coexisting chaotic sets, and so forth. Of most interest is the finding of coexisting attractors and multistability. Moreover, a moderate Allee effect in predators can stabilize the dynamical behavior. Finally, the hybrid feedback control strategy is implemented to stabilize chaotic orbits existing in the model.

Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/ddns/2023/5475999.pdf (application/pdf)
http://downloads.hindawi.com/journals/ddns/2023/5475999.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:5475999

DOI: 10.1155/2023/5475999

Access Statistics for this article

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