Global Dynamics of Leslie-Gower Competitive Systems in the Plane

Mustafa R. S. Kulenović and David T. McArdle
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Mustafa R. S. Kulenović: Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA
David T. McArdle: Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA

Mathematics, 2019, vol. 7, issue 1, 1-17

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.

Keywords: competitive; competitive exclusion; global stable manifold; map; monotonicity; period-two solution; unstable manifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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