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.
Citation: Anel Esquivel-Navarrete, Jorge Sanchez-Ortiz, Gabriel Catalan-Angeles, Martin P. Arciga-Alejandre. Tritrophic fractional model with Holling III functional response[J]. AIMS Mathematics, 2024, 9(6): 15937-15948. doi: 10.3934/math.2024771
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.
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Anel Esquivel-Navarrete, Jorge Sanchez-Ortiz, Gabriel Catalan-Angeles, Martin P. Arciga-Alejandre. Tritrophic fractional model with Holling III functional response[J]. AIMS Mathematics, 2024, 9(6): 15937-15948. doi: 10.3934/math.2024771
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