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