The yeast cell-cycle network is robustly designed to maintain stability and functionality. This study investigates the cell-cycle regulatory network of budding yeast, revealing that it is highly stable and resistant to small perturbations. The biological stationary state, the G1 phase, acts as a global attractor, while the cell-cycle sequence of protein states follows a globally attracting trajectory. These properties are preserved under small network perturbations, indicating the robustness of the cellular regulatory network. The cell-cycle process in budding yeast involves four phases: G1, S, G2, and M. The network regulating this process includes cyclins, inhibitors, degraders, competitors, transcription factors, and checkpoints. The network's dynamic properties are analyzed using a simplified model, where nodes represent protein states and arrows represent regulatory interactions. The model shows that the G1 state is a stable attractor, and the cell-cycle sequence follows a stable trajectory. The study compares the yeast cell-cycle network with random networks, finding that the yeast network has a larger basin of attraction and more convergence in trajectories. This suggests that the yeast network is more robust and stable. The network's robustness is further demonstrated by its resistance to perturbations, such as the deletion, addition, or switching of regulatory interactions. The results indicate that the yeast cell-cycle network is robustly designed, with the G1 state as a stable attractor and the cell-cycle sequence as a stable trajectory. These properties are essential for the reliable execution of cellular functions despite environmental variability. The study also highlights the importance of network topology in maintaining the stability and functionality of biological systems. The findings support the idea that biological systems can be modeled as dynamic systems, with biological states corresponding to attractors and pathways representing stable trajectories. The robustness of the yeast cell-cycle network underscores the evolutionary advantage of such design in ensuring the reliability of cellular processes.The yeast cell-cycle network is robustly designed to maintain stability and functionality. This study investigates the cell-cycle regulatory network of budding yeast, revealing that it is highly stable and resistant to small perturbations. The biological stationary state, the G1 phase, acts as a global attractor, while the cell-cycle sequence of protein states follows a globally attracting trajectory. These properties are preserved under small network perturbations, indicating the robustness of the cellular regulatory network. The cell-cycle process in budding yeast involves four phases: G1, S, G2, and M. The network regulating this process includes cyclins, inhibitors, degraders, competitors, transcription factors, and checkpoints. The network's dynamic properties are analyzed using a simplified model, where nodes represent protein states and arrows represent regulatory interactions. The model shows that the G1 state is a stable attractor, and the cell-cycle sequence follows a stable trajectory. The study compares the yeast cell-cycle network with random networks, finding that the yeast network has a larger basin of attraction and more convergence in trajectories. This suggests that the yeast network is more robust and stable. The network's robustness is further demonstrated by its resistance to perturbations, such as the deletion, addition, or switching of regulatory interactions. The results indicate that the yeast cell-cycle network is robustly designed, with the G1 state as a stable attractor and the cell-cycle sequence as a stable trajectory. These properties are essential for the reliable execution of cellular functions despite environmental variability. The study also highlights the importance of network topology in maintaining the stability and functionality of biological systems. The findings support the idea that biological systems can be modeled as dynamic systems, with biological states corresponding to attractors and pathways representing stable trajectories. The robustness of the yeast cell-cycle network underscores the evolutionary advantage of such design in ensuring the reliability of cellular processes.