Global dynamics of a tritrophic food chain model subject to the Allee effects in the prey population with sexually reproductive generalized‐type top predator. Issue 2 (23rd December 2019)

• Record Type: Journal Article
• Authors: Debnath, Surajit; Ghosh, Uttam; Sarkar, Susmita
• Is Part Of: Computational and mathematical methods. Volume 2:Issue 2(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-12-23
• Subjects: Allee effect -- center manifold theorem -- chaotic behavior -- Crowley‐Martin senses functional response -- global stability -- Holling type II functional response -- Hopf bifurcation -- saddle‐node bifurcation; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1079
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract : In this article, we have considered a continuous tritrophic food chain model subject to the Allee effect on the prey growth function with prey‐dependent Holling type II functional response between the prey and intermediate predator; Crowley‐Martin senses functional response between intermediate predator and top predator, and the top predator is of sexually reproductive type. We have established the positivity and boundedness of the system and the condition of existence of different equilibrium points. The local and global stability of the solutions about the various equilibrium points has been investigated. The center manifold theorem has been used to find the nature of the solution in the neighborhood of the nonhyperbolic equilibrium points and the direction of Hopf bifurcations. Numerical simulation has been carried out to establish the theoretical findings and finally some concluding remarks are given.