Open AccessGlobal dynamics of a tritrophic food chain model subject to the Allee effects in the prey population with sexually reproductive generalized‐type top predator
Author(s) -
Debnath Surajit,
Ghosh Uttam,
Sarkar Susmita
Publication year - 2020
Publication title -
computational and mathematical methods
Language(s) - English
Resource type - Journals
ISSN - 2577-7408
DOI - 10.1002/cmm4.1079
Subject(s) - allee effect , functional response , center manifold , predation , type (biology) , population , mathematics , equilibrium point , predator , hopf bifurcation , stability (learning theory) , food chain , dynamics (music) , mathematical economics , control theory (sociology) , ecology , biology , mathematical analysis , nonlinear system , economics , bifurcation , computer science , physics , sociology , acoustics , demography , control (management) , management , quantum mechanics , machine learning , differential equation
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.