Global asymptotic behavior of a two-dimensional difference equation modelling competition

By D. Clark, Mustafa R. S. Kulenovic, J. F. Selgrade. 2003

129 citations recorded by the source corpus.

We investigate the global asymptotic behavior of solutions of the system of difference equations xn+1 = xn/ a + cyn, yn+1 = yn/ b + dxn, n =0,1,..., where the parameters a and b are in (0, 1), c and d are arbitrary positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers. We show that the stable manifold of this system separates the positive quadrant into basins of attraction of two types of asymptotic behavior. In the case where a = b we find an explicit equation for the stable manifold.

Subfields: Genetics, Geometry and Topology, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/2b622258c16c9f412aa8872baf40a589c3a56940

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Senada Kalabusic
2. Esmir Pilav
3. Hal L. Smith

In Public Health, Environmental and Occupational Health

1. Senada Kalabusic
2. Esmir Pilav
3. Mehmed Nurkanovic
4. Mustafa R. S. Kulenovic
5. Hal L. Smith

Citations in the corpus

• Dynamics of a two-dimensional system of rational difference equations of Leslie--Gower type (2011, background): “Special attention to discrete competitive and cooperative systems in the plane was given in [2,3,5-7,10,12,17,20].”
• Asymptotic behavior of a competitive system of linear fractional difference equations (2006, background): “In [2] we show that when A < 1, B < 1, the stable manifold of the positive equilibrium (1− B,1−A) of system (1.”