Resumo

VALENZUELA-FIGUEROA, Sebastián; GONZALEZ-OLIVARES, Eduardo  e  ROJAS-PALMA, Alejandro. Influence of the weak allee effect on prey in a Leslie-Gower type predation model with sigmoid functional response. Rev. Mat [online]. 2022, vol.29, n.1, pp.105-138. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v29i1.48408.

Using a topologically equivalent system to the original, dependent only on four parameters, in this work we analyze a Leslie-Gower type predation model, considering that predator consumption is modeled by a sigmoid functional response. Furthermore, we assume that the prey are affected by an Allee effect and that the predators are generalists. We show that the system of ordinary differential equations (ODE) that the model describes can have up to four positive equilibrium points. Given the difficulties in obtaining explicitly the coordinates of these points, we partially analyze the system considering that the prey population is affected by a weak Allee effect. Among the most important results obtained, the existence of a separator curve is demonstrated, dividing the behavior of the solutions or trajectories of the system in the phase plane. Two very close solutions, but on a different side of that separatrix, would have different and distant ω − limit sets. This implies that having the same population size of the prey, for different population sizes of predators, but very close, both populations could coexist or the prey could go to extinction. We estimate that the analytical results obtained have an adequate ecological interpretation, under the underlying assumptions in the modeling of the predation interaction with ODEs.

Palavras-chave : predator-prey model; bifurcation; limit cycle; separatrix curve; stability; functional response..

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