Author/Authors :
El-Moneam ، M. A. - Jazan University , Ibrahim ، Tarek F. - King Khalid University , Elamody ، S. - Jazan University
Abstract :
In this paper we investigate the local stability, global stability, and boundedness of solutions of the recursive sequence x n + 1 = x n − p ( 2 x n − q + a x n − r /x n − q + a x n − r ) , where x − q + k ≠ − a x − r + k for k = 0 , 1 , … , min ( q , r ) , a ∈ R , p , q , r ≥ 0 with the initial condition x − p , x − p + 1 , … , x − q , x − q + 1 , … , x − r , x − r + 1 , … , x − 1 and x 0 ∈ ( 0 , ∞ ) . Some numerical examples will be given to illustrate our results.
Keywords :
Difference equations , prime period two solution , boundedness character , locally asymptotically stable , global attractor , global stability , high orders
