Sufficient conditions for the stability of a system of Non-linear Volterra difference equations with variable Delay

Abstract

This research seeks to obtain sufficient conditions for the zero solution of a system of non-linear Volterra difference equations with variable delay to be stable. The Lyapunov’s direct method is employed in the research to establish the sufficient conditions. In the process a suitable Lyapunov function is constructed which is then used to obtain inequalities that relate the solution of the system of difference equations. The obtained inequalities were then utilized to obtain results for which the system of non-linear Volterra difference equations has a stable zero solution. To illustrate the power of the obtained sufficient conditions, an example was constructed.