In real complex systems, the overall function is maintained through the connections among nodes. Failures of some nodes will destroy the connectivity of the system and thus damage the function of the system. In some complex systems, some nodes can form ``interdependency groups" through hidden interdependencies, and the failure of one node will damage the rest of the nodes in the interdependency group. In this paper, we investigate the effects of the interdependency strength of the nodes, the size distribution and the size of the interdependency groups on the cascading dynamics and the robustness of complex networks. Through numerical simulation and theoretical analysis, it is found that the cascading failure of the networks can be divided into two processes at the scale level: ``intra-group cascading" and ``inter-group cascading". In the process of intra-group cascading, the failure of one node will cause damage to the failure of other nodes in the group through the dependence between nodes, thus inducing the failure of more nodes and resulting in greater destructive force. In the process of intra-group cascading, the failure of one node will cause damage to other nodes in the group through the interdependence between nodes, thus inducing the failure of more nodes and resulting in greater destructive power. In the process of inter-group cascading, the failed nodes will cause the fragmentation of the networks, which leads to some nodes outside the interdependency group isolate from the giant component and go to fail. Under the synergistic effects of these two processes, it is found that there are continuous and discontinuous phase transition phenomena in the cascade dynamics of the network. The occurrence of these two kinds of phase transition phenomena is related to the interdependency strength of nodes, the network degree distribution and the size distribution of the interdependence group. This means that by controlling the characteristics of interdependency groups, such as the interdependence strength of the nodes in the interdependency group or the size distribution of interdependency groups, sudden system collapse can be avoided and thus the robustness of the network can be improved.
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