- Turkish Journal of Mathematics
- Vol: 41 Issue: 2
- Existence and global attractivity of periodic solutions in a max-type system of difference equations
Existence and global attractivity of periodic solutions in a max-type system of difference equations
Authors : Imane Dekkar, Nouressadat Touafek
Pages : 412-425
View : 8 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :We consider in this paper the following system of difference equations with maximum $$ \left\{ \begin{array}{lll} x(n+1)= & \max\{f_1(n,x(n)),g_1(n,y(n))\}& \\ & &, ~~ n=0,1,2, \ldots, \\ y(n+1)= & \max\{f_2(n,x(n)),g_2(n,y(n))\} & \\ \end{array} \right.$$ where $f_i, g_i$, $i=1,2$, are real-valued functions with periodic coefficients. We use the Banach fixed point theorem to get a sufficient condition under which this system admits a unique periodic solution. Moreover, we show that this periodic solution attracts all the solutions of the current system. Some examples are also given to illustrate our results.Keywords : Max-type difference equations, nonautonomous difference equations, periodic solutions, Banach fixed point theorem, global attractivity