Hopf bifurcations through delay in pilot reaction in a longitudinal flight

A. Halanay (1) , A. Ioniţă (2) , C.-A. Safta (3)

1 Department of Mathematics I
2 Institute for Theoretical and Experimental Analysis of Aeronautical Structures
3 Department of Hydraulics and Hydraulic Machinery

The paper is devoted to the study of pilot induced oscillations in the landing transition between the approach task and flare to touch-down. These oscillations are proved to appear in a longitudinal flight model when the delay in pilot's reactions exceeds a certain threshold for which the stability of equilibria is lost and a Hopf bifurcation appears. The formulae needed to compute the Lyapunov coefficient and an approximation of the solution are developed for the delay differential equations that model the pilot–vehicle interaction in landing task. These are applied for a concrete model.

Mots clés: Delay differential equations; Hopf bifurcation; Lyapunov coefficient; Pilot induced oscillations

A. Halanay, A. Ioniţă, C.-A. Safta. Hopf bifurcations through delay in pilot reaction in a longitudinal flight. Nonlinear Dynamics, 2010, 60 (3), pp.413-423. ⟨10.1007/s11071-009-9605-x⟩. ⟨hal-00568399⟩