Dynamics of a Higher-Order System of Difference Equations - Qi Wang; Qinqin Zhang; Qirui Li (Discrete Dynamics in Nature and Society)
Consider the following system of difference equations: xn+1(i)=xn-m+1(i)/Ai∏j=0m-1xn-j(i+j+1)+αi, xn+1(i+m)=xn+1(i), x1-l(i+l)=ai,l, Ai+m=Ai, αi+m=αi, i,l=1,2,…,m; n=0,1,2,…, where m is a positive integer, Ai,αi, i=1,2,…,m, and the initial conditions ai,l, i,l=1,2,…,m, are positive real numbers. We obtain the expressions of the positive solutions of the system and then give a precise description of the convergence of the positive solutions. Finally, we give some numerical results.