Stabilization by external pulses and synchronous response in the Rössler system before saddle-node bifurcation

The pulse driven Rössler system before the saddle-node bifurcation in the regime of divergence is considered. It is shown that external pulses initiate stable periodic and quasi-periodic regimes in non-autonomous system. The effect of synchronous response due interaction between external signal and own rhythm of autonomous system concerned with the «rotation» of the representation point in the three-dimensional phase space is observed. It is revealed that the torus doublings in the stroboscopic section exist in the certain area on the parameter plane of external force in this system.