@article{Ramos-Castellano2024, 
author = {Jorge Luis Ramos-Castellano and Miguel Angel Dela-Rosa and Iván Loreto-Hernández},
title = {Bifurcation analysis for the coexistence in a Gause-type four-species food web model with general functional responses},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {30263-30297},
keywords = {four-dimensional food web model, Hopf bifurcation, Bogdanov-Takens bifurcation, coexistence of species, generalized functional responses},
url = {https://www.sciopen.com/article/10.3934/math.20241461},
doi = {10.3934/math.20241461},
abstract = {The dynamics of an ordinary differential equations (ODEs) system modelling the interaction of four species (one prey or resource population, two mesopredator populations, and one super-predator population) was analyzed. It was assumed that the functional responses for each interaction were general. We showed parameter conditions that ensured that the differential system underwent a supercritical Hopf bifurcation or a Bogdanov-Takens bifurcation, from which the coexistence of the four species was guaranteed. In addition, the results were illustrated by several applications, where the prey had a logistic growth rate. For the interaction of the mesopredators and prey, we considered classical Holling-type functional responses, and for the rest of the interactions, we proposed certain generalized functional responses similar to the well-known "Beddington-DeAngelis" or "Crowley-Martin" functional responses. At the end, some numerical simulations were given.}
}