On the Asymptotic Stability of the Nonlinear Difference Equation System

Authors : Serbun Ufuk DEĞER, Yaşar BOLAT

Pages : 65-71

Doi:10.33187/jmsm.887537

View : 21 | Download : 9

Publication Date : 2021-08-31

Article Type : Research Paper

Abstract :In this paper, we obtain some new results on the equi-boundedness of solutions and asymptotic stability for a class of nonlinear difference systems with variable delay of the form x insert ignore into journalissuearticles values( n + 1 ); = a x insert ignore into journalissuearticles values( n ); + B insert ignore into journalissuearticles values( n ); F insert ignore into journalissuearticles values( x insert ignore into journalissuearticles values( n − m insert ignore into journalissuearticles values( n ); ); ); ,   n = 0 , 1 , 2 , . . . xinsert ignore into journalissuearticles values(n+1);=axinsert ignore into journalissuearticles values(n);+Binsert ignore into journalissuearticles values(n);Finsert ignore into journalissuearticles values(xinsert ignore into journalissuearticles values(n−minsert ignore into journalissuearticles values(n);););,\ \ \ \ \ \ n=0,1,2,... where F F is the real valued vector function, m : Z → Z + , m:Z→Z+, which is bounded function and maximum value of m m is k k and is a k × k k×k variable coefficient matrix. We carry out the proof of our results by using the Banach fixed point theorem and we use these results to determine the asymptotic stability conditions of an example.
Keywords : Asymptotic stability, Difference equation, Liapunov stable