Asymptotic stability of solutions of a system of difference equations with finite delay

Abstract

This thesis is concerned with the stability of solutions of a system of difference equations with finite delay. Fixed point theory is used in this thesis to investigate the stability of solutions of a system of difference equations with finite delay. In particular, the Banach fixed point theorem is used in the thesis. In the process the system of equations are inverted to obtain an equivalent summation equations. The result of the inversion is used to define a suitable mapping which is then used to discuss the stability properties of solutions of the system of difference equations with finite delay. Sufficient conditions that guarantee that the zero solution of a system of difference equations with finite delay are asymptotically stable are obtained.