Dynamics of a kicked oscillator with a delay in its parametric feedback loop: An analytical study

This paper deals with the behavior of a parametrically-forced analytically-solvable oscillator in the presence of a delay in the feedback loop. In spite of the delay, it is here shown that, when the system is in the strong relaxation regime, a one-dimensional approximation to the Poincaré (stroboscopic) map may be constructed. The influence of both the delay and the amplitude of the impulses on the dynamics is explained in terms of the geometric properties of either the isochrone portrait or the PTC. Interest has recently grown on this kind of excitation because in real-life feedback systems a delay is always present.