Existence and global attractivity of periodic solutions in a max-type system  of  difference equations

İmane DEKKAR; Nouressadat TOUAFEK

Article Details

Existence and global attractivity of periodic solutions in a max-type system of difference equations

Authors:

İmane DEKKAR | Nouressadat TOUAFEK

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2017 Vol.41 Issue 2, pp.412-425

Document Type:

Article

Publication Date:

3/2017

Document Language:

Turkish

Document ID (Org No.):

2000746077

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Abstract:

 

We consider  in this paper the following  system of difference  equations with maximum  ⎧⎪⎨⎪⎩x(n+1)=max{f1(n,x(n)),g1(n,y(n))},  n=0,1,2,…,y(n+1)=max{f2(n,x(n)),g2(n,y(n))}{x(n+1)=max{f1(n,x(n)),g1(n,y(n))},  n=0,1,2,…,y(n+1)=max{f2(n,x(n)),g2(n,y(n))} \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   fi,gifi,gif_i, g_i, i=1,2i=1,2i=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.

Article Details

Existence and global attractivity of periodic solutions in a max-type system of difference equations

Authors: İmane DEKKAR | Nouressadat TOUAFEK

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2017 Vol.41 Issue 2, pp.412-425

Document Type: Article

Publication Date: 3/2017

Document Language: Turkish

Document ID (Org No.): 2000746077

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Issues

Authors:

İmane DEKKAR | Nouressadat TOUAFEK

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2017 Vol.41 Issue 2, pp.412-425

Document Type:

Article

Publication Date:

3/2017

Document Language:

Turkish

Document ID (Org No.):

2000746077

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098