Multiple Attractors for a Competitive System of Rational Difference Equations in the Plane. (22nd November 2011)

• Record Type: Journal Article
• Authors: Kalabušić, S.; Kulenović, M. R. S.; Pilav, E.
• Other Names: Shi Yuming Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2011(2011)
• Publication Date: 2011-11-22
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2011/295308
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We investigate global dynamics of the following systems of difference equationsx n + 1 = β 1 x n / ( B 1 x n + y n ), y n + 1 = ( α 2 + γ 2 y n ) / ( A 2 + x n ), n = 0, 1, 2, …, where the parametersβ 1, B 1, β 2, α 2, γ 2, A 2 are positive numbers, and initial conditionsx 0 andy 0 are arbitrary nonnegative numbers such thatx 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.