Stability in a modified Leslie-Gower type predation model considering competence among predators




Predator-prey model, functional response, bifurcation, limit cycle, separatrix curve, stability


In the ecological literature, the interference (self-interference) or competition among predators to effect the harvesting of their prey has been modeled by different mathematical formulations.

In this work, we will establish the dynamical properties of the Leslie-Gower type predation model, in which is incorporated one of these form, described by the function b (y) = yalfa
, with 0 < alfa < 1.

The main difficulty of the analysis is due to this function is not differentiable for y = 0, and the Jacobian matrix is not defined in the equilibrium points over the horizontal axis (x-axis).

Previously, we showed a summary with the fundamental properties of the Leslie-Gower type model, in order to carry out an adequate comparative analysis with models where self-interference between predators is incorporated.

To reinforce our results, some numerical simulations are shown.


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How to Cite

González-Olivares, E., & Gallegos-Zuñiga, J. (2020). Stability in a modified Leslie-Gower type predation model considering competence among predators. Selecciones Matemáticas, 7(01), 10-24.

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