Asymptotic behavior of a competitive system of linear fractional difference equations

Authors

Mustafa Kulenovic, University of Rhode IslandFollow
M. Nurkanović

Document Type

Article

Date of Original Version

2006

Abstract

We investigate the global asymptotic behavior of solutions of the system of difference equations x_n+1 = (a+x _n )/(b+y _n ), y_n+1 = (d+y _n )/(e+x _n ), 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.

Citation/Publisher Attribution

Kulenović, M. R.S., & Nurkanović, M. (2006). Asymptotic behavior of a competitive system of linear fractional difference equations. Advances in Difference Equations, 2006, Article ID 19756. doi: 10.1155/ADE/2006/19756

Available at: http://dx.doi.org/10.1155/ADE/2006/19756

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.