Co-dimension 2 bifurcation analysis of a tri-trophic food chain model with strong Allee effect and Crowley–Martin functional response

Siti Nurnabihah Karim and Tau Keong Ang

Chaos, Solitons & Fractals, 2024, vol. 186, issue C

Abstract: This paper focuses on the species interaction within a tri-trophic food chain model involving species’ mutual interference, characterized by Crowley–Martin functional response with strong Allee effect in prey species. First, the evaluation of the solutions’ positivity and boundedness is conducted. Subsequently, the local stability of equilibrium points is analysed, and the Lyapunov function is employed to assess the global stability of interior equilibrium. We have also established adequate criteria for detecting local bifurcations. Sotomayor’s theorem infers the presence of saddle–node and transcritical bifurcations. Utilizing the centre manifold theory and the Hopf bifurcation theorem, the emergence and stability of Hopf bifurcation are investigated. Following this, numerical simulations are performed so as to validate the theoretical findings and analyse the impacts of Allee effect in greater details. The analysis reveals that the system undergoes a range of local bifurcations in co-dimension one, including saddle–node, subcritical and supercritical Hopf bifurcations. Furthermore, the existence of global dynamics can be observed by the appearance of Generalized-Hopf bifurcation in the co-dimension two bifurcation diagram. The findings suggest that strong Allee effect could trigger instability and induce a bi-stability phenomenon in the system’s dynamical behaviours.

Keywords: Strong Allee effect; Crowley–Martin functional response; Sotomayor’s theorem; Hopf bifurcation theorem; Generalized-Hopf; Bi-stability (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077924008683
Full text for ScienceDirect subscribers only

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:eee:chsofr:v:186:y:2024:i:c:s0960077924008683

DOI: 10.1016/j.chaos.2024.115316

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().