Computation of frequency locking regions for a discontinuous periodically forced reactor

The interaction between an external periodic forcing and the natural frequencies of a reactor or system of reactors can give rise to an interesting dynamic behaviour. Particularly, the system may develop subharmonic regimes (also called resonant regimes, where the periods are exact multiples of the period of the forcing), quasi-periodic regimes and chaos. In this work, frequency locking phenomena, that is transitions between quasi-periodic regimes and resonant regimes are studied for a reactor with discontinuously and periodically forced feed. In the parameter space, regions containing resonant regimes (Arnold tongues) can be detected by means of automatic parameter continuation. The difficulties related to the discontinuous nature of the forcing are overcome by applying continuation algorithms to the (smooth) Poincaré map of the system. The relationship between Floquet multipliers and rotation number of the corresponding resonant regimes is exploited to readily locate the cusps of resonance regions in a two-parameter space.