A discrete-time dynamical system of wild mosquito population with Allee effects

We study a discrete-time dynamical system of wild mosquito population with parameters: $β$ - the birth rate of adults; $α$ - maximum emergence rate; $μ>0$ - the death rate of adults; $γ$ - Allee effects. We prove that if $γ\geq\frac{α(β-μ)}{μ^2}$ then the mosquito population dies and if $γ<\frac{α(β-μ)}{μ^2}$ holds then extinction or survival of the mosquito population depends on their initial state.

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