Delay differential equations and their applications: analysis and numerical investigation of oscillatory behaviours

Abstract

This project focuses on the analysis of Delay Differential Equations (DDEs) to investigate the impact of time delays on system dynamics. By studying the stability, oscillatory behavior and bifurcations introduced by these delays, the study aims to develop a deeper understanding of how delays affect different systems. Due to the complexity of DDEs, the analysis requires advanced techniques such as linearization, as well as both analytical and numerical simulations. Understanding DDEs is crucial as they are widely applicable in fields such as biology, engineering and control systems.