Influence of the strong Allee effect on prey and the competition among predators in Leslie-Gower type predation models
Keywords:Predator-prey model, functional response, bifurcation, limit cycle, separatrix curve, stability
It is well known that predator-prey interactions are strongly dependent on the functional response as well as the population growth rates of prey and predators.
In this work, the study will be based on a Leslie-Gower type predation model, described by a twodimensional system of ordinary differential equations (ODEs), assuming the prey population is affected by a strong Allee effect and that predators have an alternative food.
The functional response will be assumed linear, which is prey-dependent and monotonously increasing. In turn, the equation of growth of predators will also be considered of the logistic type, where the environmental carrying capacity for predators is assumed proportional to the prey population size. Among the most important results obtained is that for a same set of parameters, there are different behaviors of the system solutions, since two attractor equilibrium points can exist. Then, populations can coexist around of fixed population sizes, or the prey population can become extinct. 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.
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