INVESTIGATION OF THE PERIODICITY AND STABILITY OF SOLUTIONS FOR CERTAIN DELAY FUNCTIONAL NEUTRAL DIFFERENTIAL SYSTEMS

This study investigates the stability and existence of periodic solutions in neutral differential systems with time delays and variable coefficients. By utilizing Krasnoselskii’s fixed point theorem, we demonstrate a set of sufficient conditions ensuring the existences of such a periodic solution. This involves transforming the system into an equivalent integral form before applying the fundamental matrix solutions alongside Floquet theory. In addition, we will analyze the asymptotic stability of these solutions, thus establishing new conditions that can ensure stability. The practical relevance of our theoretical results is supported through numerical examples, validating the proposed approach, and highlighting its suitability in areas such as electrical circuits, control systems, and biological modeling. This study extends previous work and thereby offers a detailed framework intended for use in studying neutral differential systems where time delays are present.