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Discontinuity, Nonlinearity, and Complexity 13(3) (2024) 495--506 | DOI:10.5890/DNC.2024.09.008

U. A. Rozikov, Z.S. Boxonov

V.I. Romanovskiy Institute of Mathematics of Uzbek Academy of Sciences

Central Asian University, 264, Milliy bog St, 111221, Tashkent, Uzbekistan

Faculty of Mathematics, National University of Uzbekistan

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Abstract

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

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