Global Dynamics of Leslie-Gower Competitive Systems in the Plane

Global dynamic results are obtained for families of competitive systems of difference equations of the form x n + 1 = b 1 x n α 1 + x n + c 1 y n , y n + 1 = b 2 y n α 2 + c 2 x n + y n n = 0 , 1 , … , where the parameters b 1 , b 2 are positive numbers, and α 1 , α 2 , c 1 , and c 2 and the initial conditions x 0 and y 0 are arbitrary non-negative numbers, when one or both of α i , i = 1 , 2 equalls 0. We assume that the denominators of both equations are always positive. We will show that the presence of more parameters will create more dynamic scenarios.