Asymptotic behavior of a competitive system of linear fractional difference equations
By Mustafa R. S. Kulenovic, Mehmed Nurkanovic. 2006
59 citations recorded by the source corpus.
We investigate the global asymptotic behavior of solutions of the system of difference equations xn+1 = (a+xn)/(b+yn), yn+1 = (d+yn)/(e+xn), n = 0,1,..., where the parameters a, b, d, and e are positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers. In certain range of parameters, we prove the existence of the global stable manifold of the unique positive equilibrium of this system which is the graph of an increasing curve. We show that the stable manifold of this system separates the positive quadrant of initial conditions into basins of attraction of two types of asymptotic behavior. In the case where a = d and b = e, we find an explicit equation for the stable manifold to be y = x.
Subfields: Applied Mathematics, Geometry and Topology, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/9ace5f05d625dda63ae420d2ea7aeba176b5920a
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Citations in the corpus
- Dynamic behavior of a second-order nonlinearrational difference equation (2015, background): “Solving difference equations and studying the asymptotic behavior of their solutions has attracted the attention of many authors, see for example [1, 3, 4, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31].”
- On a k-Order System of Lyness-Type Difference Equations (2007, background): “So there exist many papers concerning systems of difference equations (see [1–10] and the references cited therein).”