Turkish Journal of Mathematics
Existence and global attractivity of periodic solutions in a max-type system of difference equations
DOI
10.3906/mat-1601-62
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
First Page
412
Last Page
425
Recommended Citation
DEKKAR, IMANE and TOUAFEK, NOURESSADAT
(2017)
"Existence and global attractivity of periodic solutions in a max-type system of difference equations,"
Turkish Journal of Mathematics: Vol. 41:
No.
2, Article 18.
https://doi.org/10.3906/mat-1601-62
Available at:
https://journals.tubitak.gov.tr/math/vol41/iss2/18
