Abstract
The main objective of this paper is to study the global stability of the positive solutions and the periodic character of the difference equation
x(n+1) = ax(n), + alpha x(n)x(n-l)/beta x(n) + gamma x(n-k), n = 0, 1, ...,
where the parameters alpha, beta, gamma and a are positive real numbers and the initial conditions x(-t), x(-t+1) ..., x(-1) and xo are positive real numbers where t = max{l, k}. Numerical examples to the difference equation are given to explain our results.