A remark on " Global dynamics of a tritrophic food chain model subject to the Allee effects in the prey population with sexually reproductive generalized‐type top predator" [Comp and Math Methods. 2019; E1079, pp. 1–23]. Issue 5 (2nd April 2021)

• Record Type: Journal Article
• Authors: Takyi, Eric M.; Antwi‐Fordjour, Kwadwo; Kouachi, Said; Parshad, Rana D.
• Is Part Of: Computational and mathematical methods. Volume 3:Issue 5(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-04-02
• Subjects: Allee effect -- finite time blow up -- three species food chain; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1159
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract: In Debnath et al. (2019), a tritrophic food chain model subject to a Allee effect on the prey growth and Crowley–Martin senses functional response between intermediate predator and top predator, with a top predator of sexually reproductive type is considered. It is claimed that under certain restrictions on the parameter space, the model has bounded solutions for all positive initial conditions, and is dissipative. We show that this is not true. In particular, solutions to the model can blow‐up in finite time, even under the restrictions derived in Debnath et al. (2019), for sufficiently chosen initial data. We derive a new extinction boundary for the system. We also conjecture on the effect of the Allee threshold on the blow‐up dynamics in the model. All of our results are validated via numerical simulations.