Dynamics of a Higher-Order System of Difference Equations

Abstract

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,…,wheremis a positive integer,Ai,αi,i=1,2,…,m, and the initial conditionsai,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.

Dynamic Characteristics of Four Systems of Difference Equations with Higher Order

“…On the other hand, in recent years, many works have been published that discussed dynamic behavior of difference equation along their systems [15][16][17][18][19][20]. In continuation of existing study, it is important to mention that dynamical characteristics of the following difference equation have been investigated by Bajo and Liz [21]:…”