Global stability in a modified Leslie-Gower type predation model assuming mutual interference among generalist predators
Autor
Rojas-Palma, Alejandro
Gonzáles Olivares, Eduardo
Fecha
2020Resumen
In the ecological literature, mutual interference (self-interference) or competition among predators (CAP) to effect the harvesting of their prey has been modeled through different mathematical formulations. In this work, the dynamical properties of a Leslie-Gower type predation model is analyzed, incorporating one of these forms, which is described by the function g(y)=yβ, with 0<β<1. This function g is not differentiable for y=0, and neither the Jacobian matrix of the system is not defined in the equilibrium points over the horizontal axis (x−axis). To determine the nature of these points, we had to use a non-standard methodology. Previously, we have shown the fundamental properties of the Leslie-Gower type model with generalist predators, to carry out an adequate comparative analysis with the model where the competition among predators (CAP) is incorporated. The main obtained outcomes in both systems are: (ⅰ) The unique positive equilibrium point, when exists, is globally asymptotically stable (g.a.s), which is proven using a suitable Lyapunov function. (ⅱ) There not exist periodic orbits, which was proved constructing an adequate Dulac function.
Fuente
Mathematical Biosciences and Engineering, 17(6), 7708-7731Link de Acceso
Click aquí para ver el documentoIdentificador DOI
doi.org/10.3934/mbe.2020392Colecciones
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