1. Tritrophic fractional model with Holling III functional response
- Author
-
Anel Esquivel-Navarrete, Jorge Sanchez-Ortiz, Gabriel Catalan-Angeles, and Martin P. Arciga-Alejandre
- Subjects
caputo fractional derivative ,routh-hurwitz criterion ,tritrophic model ,lotka-volterra ,homotopic perturbation method ,Mathematics ,QA1-939 - 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.
- Published
- 2024
- Full Text
- View/download PDF