Document Type
Article
Date of Original Version
12-1-2011
Abstract
We investigate global dynamics of the following systems of difference equations x n + 1 = 1 x n / (B 1 x n + y n), y n + 1 = ( 2 + 2 y n) / (A 2 + x n), n = 0, 1, 2, , where the parameters 1, B 1, 2, 2, 2, A 2 are positive numbers, and initial conditions x 0 and y 0 are arbitrary nonnegative numbers such that x 0 + y 0 0. We show that this system has up to three equilibrium points with various dynamics which depends on the part of parametric space. We show that the basins of attractions of different locally asymptotically stable equilibrium points or nonhyperbolic equilibrium points are separated by the global stable manifolds of either saddle points or of nonhyperbolic equilibrium points. We give an example of globally attractive nonhyperbolic equilibrium point and semistable non-hyperbolic equilibrium point. Copyright © 2011 S. Kalabui et al.
Publication Title, e.g., Journal
Abstract and Applied Analysis
Volume
2011
Citation/Publisher Attribution
Kalabušić, S., M. R. Kulenovič, and E. Pilav. "Multiple attractors for a competitive system of rational difference equations in the plane." Abstract and Applied Analysis 2011, (2011). doi: 10.1155/2011/295308.
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.