Analysis of a fractional-order predator-prey model with harvest incorporating an Allee effect | ||||
| Journal of Fractional Calculus and Applications | ||||
| Volume 14, Issue 2, July 2023, Page 1-14 PDF (617.06 K) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/jfca.2023.204624.1010 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
Melani Barrios  1; Daiana Bravo2; Gabriela Reyero3
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| 1Departamento de Matematica, Facultad de Ciencias Exactas. Ingenieria y Agrimensura, Universidad Nacional de Rosario, Rosario, Santa Fe, Argentina | ||||
| 2Departamento de Matematica, Facultad de Ciencias Exactas, Ingenieria y Agrimensura, Universidad Nacional de Rosario, Rosario, Argentina. | ||||
| 3Departamento de Matematica, Facultad de Ciencias Exactas, Ingenieria y Agrimensura, Universidad Nacional de Rosario, Rosario, Argentina | ||||
| Abstract | ||||
| The objective of this work is to model a population management in which two species intervene. There is an interdependence predator-prey relationship between them. It will be assumed, as a descriptive biological model, the Lotka-Volterra one with the application of an Allee effect in one of the dynamics of the species. This incorporation into the system make the model more realistic. In view of the advantages, the model will be in its fractional version, that is, where derivatives of Caputo of fractional order are considered, with the fractional order in (0,1]. Existence and uniqueness of the model solution will be explicitly proved, and a non-negative invariance of the solution and the stability of the resulting equilibrium will be studied. In order to solve the problem, the use of fractional numerical techniques will be of fundamental importance and absolutely essential to conclude the analysis. Some examples of great importance will be shown. | ||||
| Keywords | ||||
| Caputo derivatives; Lotka-Volterra; biological model; natural resources management | ||||
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