@article{Esquivel-Navarrete2024, 
author = {Anel Esquivel-Navarrete and Jorge Sanchez-Ortiz and Gabriel Catalan-Angeles and Martin P. Arciga-Alejandre},
title = {Tritrophic fractional model with Holling III functional response},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {15937-15948},
keywords = {Caputo fractional derivative, Routh-Hurwitz Criterion, tritrophic model, Lotka-Volterra, homotopic perturbation method},
url = {https://www.sciopen.com/article/10.3934/math.2024771},
doi = {10.3934/math.2024771},
abstract = {In this paper, we analyzed the local stability of three species in two fractional tritrophic systems, with Caputo's fractional derivative and Holling type Ⅱ and Ⅲ functional responses, when the prey density has a linear growth. To begin, we obtained the equilibria in the first octant under certain conditions for the parameters. Subsequently, through linearization and applying the Routh-Hurwitz Criterion, we concluded that only the system with Holling type Ⅲ exhibits an asymptotically stable equilibrium point, where the fractional derivative order belongs to the interval    (  0  ,  1  ]. Finally, we obtained the solution of the system with the Holling type Ⅲ functional response, using the multistage homotopic perturbation method, and presented an example that shows the dynamics of the solutions around the stable equilibrium point.}
}