On the Psi -Instability of a Non-Linear Difference System

Abstract

The objective of this work to give sufficient condition for on Instability of nonlinear difference system

x(m+1) = A (m) x(m) +f (m, x(m))                             (1.1)

and the linear difference system of the form

x(m+1) = A (m) x(m) +B (m) x(m)                              (1.2)

As a perturbed system of x (m+1) =A(m) x (m)          (1.3)

In equation (1.1) and (1.2) we consider that A(m) and B(m)  are  n ×n matrix valued mappings on N and f is a vector  function of order n on N