Stabilization of the less stable orbit by a tiny near-resonance periodic signal

In this paper, a tiny near-resonance periodic signal is used to stabilize the less stable state under perturbation. Under the action of this external signal, the basin of the period-3 state is extended greatly. Joint use of signal and noise can enhance the stabilization effectiveness of the periodic signal. The sensitive dependence of the effectiveness on signal frequency shows that this stabilization may be due to a certain resonancelike behavior. Numerical calculations also show that the shape of the signal is not an essential factor in our method. This allows a free selection of the applied signal. The method is suitable for driving the system to the less stable state of a pair of coexisting states.