Analysis of the dynamics of a delay system modeling a longitudinal flight

The paper is devoted to the study of PIO (pilot induced oscillations) in a longitudinal flight. The phenomenon of PIO is the interaction between aircraft's motion and the pilot. PIO are present more often in terminal flight conditions. Using the qualitative theory of delay differential equations, a conventional time-delay model is considered and the stability of the equilibrium is analyzed. A limit cycle is shown to appear by a Hopf bifurcation.