- Journal of Mathematical Sciences and Modelling
- Vol: 4 Issue: 2
- On the Asymptotic Stability of the Nonlinear Difference Equation System
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 : 18 | Download : 11
Publication Date : 2021-08-31
Article Type : Research
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 ( n + 1 ) = a x ( n ) + B ( n ) F ( x ( n − m ( n ) ) ) , n = 0 , 1 , 2 , . . . x(n+1)=ax(n)+B(n)F(x(n−m(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