Abstract
We investigate the classical Leslie-Gower competition system where one of the two competing populations is subject to Allee effects and is also under constant stocking. The model can have either no interior steady state, a unique interior steady state, two interior steady states or three interior steady states depending on parameter values. Using the tools of monotone planar systems, we provide basins of attraction for the local attractors and for the non-hyperbolic steady states. It is concluded that stocking of the weaker competitor can promote the coexistence of both competing populations.
Highlights
The Allee effect, referring to the reduced fitness or the decline in population growth at low population densities or sizes, was first observed by Allee [ ]
When a population is subject to Allee effects, it is well known that there exists a critical population level below which the population will go extinct [ ]
We consider the classical two-dimensional Leslie-Gower competition system where one of the populations is subject to Allee effects and is under constant stocking
Summary
The Allee effect, referring to the reduced fitness or the decline in population growth at low population densities or sizes, was first observed by Allee [ ]. We consider the classical two-dimensional Leslie-Gower competition system where one of the populations is subject to Allee effects and is under constant stocking. The model with no stocking has been studied in [ ]; it can have at most two interior steady states It is proved in [ ] that one of the interior steady states is a saddle point and its global stable manifold is the boundary for population coexistence and competitive exclusion. With stocking, it is shown in the present study that the model can have up to three interior steady states, one of which is a saddle point and the other two are local attractors.
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