Global Dynamics of a Competitive System of Rational Difference Equations in the Plane

Authors

S. Kalabušic
Mustafa R. Kulenović, University of Rhode IslandFollow
E. Pilav

Document Type

Article

Date of Original Version

2009

Abstract

We investigate global dynamics of the following systems of difference equations x_n+1 = (a₁ + β₁x_n)/y_n, y_n+1 = (a₂ + y₂y_n)/(A₂ + x_n), n = 0, 1, 2, …, where the parameters a₁, β₁, a₂, y₂, and A₂ are positive numbers and initial conditions X₀ and Y₀ are arbitrary nonnegative numbers such that Y₀ > 0. We show that this system has rich dynamics which depend on the part of parametric space. We show that the basins of attractions of different locally asymptotically stable equilibrium points are separated by the global stable manifolds of either saddle points or of nonhyperbolic equilibrium points.

Citation/Publisher Attribution

Kalabušić, S., Kulenović, M. R. S., & Pilav, E. (2009). Global Dynamics of a Competitive System of Rational Difference Equations in the Plane. Advances in Difference Equations, 2009, Article ID: 132802. doi: 10.1155/2009/132802

Available at: https://doi.org/10.1155/2009/132802

Creative Commons License

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