Giunta، ValeriaDighriri, Fatimah Hassan2025-03-112024https://hdl.handle.net/20.500.14154/75006Delay differential equations have been a case of curiosity to researchers for many decades. They rely on previous data and enable real-time adjustments to improve and correct systems. This thesis studies delay differential equations, analyses their behaviour, and applies them to biological population dynamics. The effect of time delay on the stability and instability of solutions is also studied, and to simulate the differential delay equations numerically, we use MATLAB.70enDelay differential equationsthe characteristic equationoscillationpopulation modelsthe continuous logistic equation.Thesis