Dynamics of a modified Leslie-Gower predation model considering a generalist predator and the hyperbolic functional response
The paper studies the following modified Leslie--Gower type model \begin{align*} \dot x &=\left(r_1 - b_1x - \frac{a_1 y}{x+k_1}\right)x,\\ \dot y &= \left( r_2 - \frac{a_2 y}{x+ k_2}\right) y, \tag{1}\end{align*} where \(x\) and \(y\) represent the size of the prey and predator population, respectively, and the parameters \(r_1, b_1, a_1, k_1, r_2, a_2, k_2\) are assumed to be positive. The authors determine the number and stability of the (biologically relevant) equilibria and show that in certain parameter regions limit cycles arise as a result of either a Hopf or a homoclinic bifurcation. The stability of these limit cycles is also analyzed. The results illustrate that system (1) has the flexibility to model several different population dynamical phenomena.
scientific article; zbMATH DE number 7381747
scientific article