Global dynamics of a Leslie host-parasite model

We consider the system of difference equations x(n+1) = alpha x(n)/1 + beta y(n), y(n+1) = gamma x(n)y(n)/x(n) + delta y(n), n = 0, 1, 2, . . . , where alpha, beta, gamma, delta, x(0), y(0) are positive real numbers. This system was formulated by P.H. Leslie in 1948 and the present manuscript provides the most complete dynamical analysis to date. A boundedness and persistence result along with global attractivity results for various parameter regions are established.