Before revision:  Then, through nonlinear dynamical analysis we demonstrate that the yeast cell-cycle process is an excited system driven by a sequence of saddle-node bifurcations with ghost effects , and the yeast cell-cycle trajectory is globally attractive with modularity in both state and parameter space, while the convergent manifold provides a suitable control state for cell-cycle checkpoints.
After revision:  Then, through nonlinear dynamic analysis, we demonstrate that the yeast cell-cycle process is an excited system driven by a sequence of saddle-node bifurcations with ghost effects , and the yeast cell-cycle trajectory is globally attractive with modularity in both state and parameter space, while the convergent manifold provides a suitable control state for cell-cycle checkpoints.