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Mathematics 2019, 7(1), 76; https://doi.org/10.3390/math7010076

Global Dynamics of Leslie-Gower Competitive Systems in the Plane

Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA
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Received: 5 December 2018 / Revised: 4 January 2019 / Accepted: 9 January 2019 / Published: 12 January 2019
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Abstract

Global dynamic results are obtained for families of competitive systems of difference equations of the form x n + 1 = b 1 x n α 1 + x n + c 1 y n , y n + 1 = b 2 y n α 2 + c 2 x n + y n n = 0 , 1 , , where the parameters b 1 , b 2 are positive numbers, and α 1 , α 2 , c 1 , and c 2 and the initial conditions x 0 and y 0 are arbitrary non-negative numbers, when one or both of α i , i = 1 , 2 equalls 0. We assume that the denominators of both equations are always positive. We will show that the presence of more parameters will create more dynamic scenarios. View Full-Text
Keywords: competitive; competitive exclusion; global stable manifold; map; monotonicity; period-two solution; unstable manifold competitive; competitive exclusion; global stable manifold; map; monotonicity; period-two solution; unstable manifold
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Kulenović, M.R.S.; McArdle, D.T. Global Dynamics of Leslie-Gower Competitive Systems in the Plane. Mathematics 2019, 7, 76.

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