The bifurcation diagram for the coupling strength k. (A) Bifurcation diagram for the coupling strength k. When the coupling strength is increased to the range between two saddle-node bifurcations, the coupled system can exhibit bistability and also exhibits some hysteresis, i.e., CDK1 converges to a low or a high state depending on the initial conditions. But when k is set to 1.6 and the synthetic rate α1 of CDK1 is changed into the square wave signal, the coupled system behaviors as (B): a pulse input drives CDK1 into the upper state and then oscillates, or oscillates all the time which depends on the initial state of the coupled system. (C) The bifurcation diagram for k when K2 = 0.35, α3 = 1.6 and other parameters are set as Table 1. (D) shows that the pulse input drives CDK1 into the upper state and cannot get back. SN: Saddle-Node point. HB: Hopf bifurcation point.