Deltaic channel networks are important conduits for water and material supplies to the fluvial and coastal communities. However, increasing human interventions in river deltas have altered the topology and geometry of channel networks as well as their long-term evolution. While the morphological evolution of a single channel has received extensive studies, the system-wide morphological responses of channel networks to local disturbances remain largely unclear. Here we investigate the morphological responses of a bifurcating channel network subject to local disturbance of channel deepening due to dredging and sand mining through idealized simulations, and further compare the results with the reference scenarios of a single channel and theoretical analysis of the phase plane. The results show that the infilling of the local deepening is associated with the erosion of the entire branch, which also causes system-wide effects on the siltation of the other branch. The morphological responses of the bifurcating channel network consist of a relatively short stage for the infilling of the local deepening followed by a relatively long stage for recovering the equilibrium configuration of the river bifurcation. The system-wide effects of the local disturbance arise from the altered water surface slope and water partitioning downstream of the bifurcation due to the local deepening. Also, the prolonged recovery of the equilibrium configuration is consistent with theoretical analysis, which reveals a slow evolution of the bifurcation when approaching the equilibrium. Our results can help understand the long-term morphological responses of large-scale complex channel networks and inform water managements under increasing human interventions.