Basins of attraction for two-species competitive model with quadratic terms and the singular Allee effect
type: Item
instance of: scholarly article
title: Basins of attraction for two-species competitive model with quadratic terms and the singular Allee effect
zbMATH Open document ID: 1418.92087
DOI: 10.1155/2015/847360
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: Summary: We consider the following system of difference equations: \(x_{n + 1} = x_n^2 / \left(B_1 x_n^2 + C_1 y_n^2\right), y_{n + 1} = y_n^2 / \left(A_2 + B_2 x_n^2 + C_2 y_n^2\right), n = 0, 1, \ldots, \) where \(B_1\), \(C_1\), \(A_2\), \(B_2\), \(C_2\) are positive constants and \(x_0, y_0 \geq 0\) are initial conditions. This system has interesting dynamics and it can have up to seven equilibrium points as well as a singular point at \((0,0)\), which always possesses a basin of attraction. We characterize the basins of attractions of all equilibrium points as well as the singular point at \((0,0)\) and thus describe the global dynamics of this system. Since the singular point at \((0,0)\) always possesses a basin of attraction this system exhibits Allee's effect.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 7025521
author: Ann Brett
author: Mustafa R. S. Kulenovic
MaRDI profile type: Publication
Wikidata QID: Q59105504
full work available at URL: https://doi.org/10.1155/2015/847360
OpenAlex ID: W2115091590
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description: scientific article; zbMATH DE number 7025521