On the system of two difference equations xn+1=∑i=0kAi/yn−ipi, yn+1=∑i=0kBi/xn−iqi

AbstractIn this paper we study the system of two difference equations of the form xn+1=∑i=0kAiyn−ipi,yn+1=∑i=0kBixn−iqi, where Ai,Bi, i∈{0,1,…,k}, xi,yi, i=−k,−k+1,…,0, are positive numbers and pi,qi, i=0,…,k, are positive constants. More precisely, we investigate the boundedness, the persistence of the positive solutions, the existence of a unique positive equilibrium and the global asymptotic stability of the positive equilibrium of the above system. Finally, we find solutions of the system which do not oscillate about the positive equilibrium