Dynamics of a two-dimensional system of rational difference equations of Leslie--Gower type

• Published in: Advances in difference equations Vol. 2011; no. 1; pp. 1 - 29
• Main Authors: Kalabušić, S, Kulenović, MRS, Pilav, E
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 23.08.2011; Springer Nature B.V; BioMed Central Ltd; SpringerOpen
• Subjects: Analysis; Asymptotic properties; Attraction; Basin of attraction; Basins; Competitive map; Difference and Functional Equations; Difference equations; Dynamical systems; Dynamics; Functional Analysis; Global stable manifold; Manifolds; Mathematical analysis; Mathematics; Mathematics and Statistics; Monotonicity; Ordinary Differential Equations; Partial Differential Equations; Period-two solution; Basin of attraction; Global stable manifold; Competitive map; Period-two solution; Monotonicity

We investigate global dynamics of the following systems of difference equations x n + 1 = α 1 + β 1 x n A 1 + y n y n + 1 = γ 2 y n A 2 + B 2 x n + y n , n = 0 , 1 , 2 , … where the parameters α 1 , β 1 , A 1 , γ 2 , A 2 , B 2 are positive numbers, and the initial conditions x 0 and y 0 are arbitrar...