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- W2890124670 abstract "We study the consequences of an Allee effect acting on the prey species in a Leslie–Gower predator–prey model. For this goal we make extensive use of analytical tools from dynamical systems theory complemented with a numerical bifurcation analysis. By studying the dynamics at infinity under a suitable compactification we prove that the model is well-posed in the sense that all the solutions are bounded. We provide a thorough analysis of the number and stability of equilibrium points. In particular, the origin is a non-hyperbolic equilibrium and presents different regimes of local (un)stability depending on certain conditions on the model parameters. In addition, we find curves of homoclinic, Hopf, and saddle–node bifurcations around a Bogdanov–Takens point. In this process, our findings indicate that the survival threshold for both populations in the two-dimensional phase space can be either a limit cycle, a homoclinic orbit, or the stable manifold of a saddle-equilibrium." @default.
- W2890124670 created "2018-09-27" @default.
- W2890124670 creator A5049028844 @default.
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- W2890124670 date "2019-02-01" @default.
- W2890124670 modified "2023-10-10" @default.
- W2890124670 title "Allee effect acting on the prey species in a Leslie–Gower predation model" @default.
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- W2890124670 doi "https://doi.org/10.1016/j.nonrwa.2018.08.009" @default.
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