Bifurcation and Global Dynamics of a Leslie-Gower Type Competitive System of Rational Difference Equations with Quadratic Terms. (2nd August 2017)

• Record Type: Journal Article
• Authors: Hadžiabdić, V.; Kulenović, M. R. S.; Pilav, E.
• Other Names: Wong Patricia J. Y. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2017(2017)
• Publication Date: 2017-08-02
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2017/3104512
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We investigate global dynamics of the following systems of difference equations x n + 1 = x n / A 1 + B 1 x n + C 1 y n, y n + 1 = y n 2 / A 2 + B 2 x n + C 2 y n 2, n = 0, 1, …, where the parameters A 1, A 2, B 1, B 2, C 1, and C 2 are positive numbers and the initial conditions x 0 and y 0 are arbitrary nonnegative numbers. This system is a version of the Leslie-Gower competition model for two species. We show that this system has rich dynamics which depends on the part of parametric space.