@article{González-Olivares_Rojas-Palma_González-Yañez_2017, title={Multiple limit cycles in a Leslie–Gower-type predator–prey model considering weak Allee effect on prey}, volume={22}, url={https://www.journals.vu.lt/nonlinear-analysis/article/view/13391}, DOI={10.15388/NA.2017.3.5}, abstractNote={<p>In this work, a modified Leslie–Gower-type predator–prey model is analyzed, considering now that the prey population is affected by a <em>weak Allee effect</em>, complementing results obtained in previous papers in which the consequences of strong Allee effect for the same model were established.<br>In order to simplify the calculations, a diffeomorphism is constructed to obtain a topological equivalent system for which we establish the boundedness of solutions, the nature of equilibrium points, the existence of a separatrix curve dividing the behavior of trajectories. Also, the existence of two concentric limit cycles surrounding a unique positive equilibrium point (generalized Hopf or Bautin bifurcation) is shown.<br>Although the equilibrium point associated to the weak Allee effect lies in the second quadrant, the model has a rich dynamics due to this phenomenon, such as it happens when a strong Allee effect is considered in prey population.<br>The model here analyzed has some similar behaviors with the model considering strong Allee effect, having both two limit cycles; nevertheless, they differ in the amount of positive equilibrium points and the existence in our model of a non-infinitesimal limit cycle, which exists when the positive equilibrium is a repeller node. The main results obtained are reinforced by means of some numerical simulations.</p>}, number={3}, journal={Nonlinear Analysis: Modelling and Control}, author={González-Olivares Eduardo and Rojas-Palma Alejandro and González-Yañez Betsabé}, year={2017}, month={May}, pages={347-365} }