Doubling of a closed invariant curve in an impulsive Goodwin's oscillator with delay

In the present paper, we focus on the doubling of closed invariant curves associated with quasiperiodic dynamics. We consider a 5D map derived from a hybrid model originating from systems biology and containing a continuous part with time delay and pulse-modulated feedback. Using numerical bifurcation analysis, we show that doubling bifurcation takes place on a closed 2D invariant manifold. We explain how such a configuration of the phase space can be created and highlight the role of delay.