The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic.Although various critical phenomena have been found in different models,study of the connections between different percolation transitions is still lacking.Here we propose a unified framework to study the origins of the discontinuous transitions of the percolation process on interacting networks.The model evolves in generations with the result of the present percolation depending on the previous state,and thus is history-dependent.Both theoretical analysis and Monte Carlo simulations reveal that the nature of the transition remains the same at finite generations but exhibits an abrupt change for the infinite generation.We use brain functional correlation and morphological similarity data to show that our model also provides a general method to explore the network structure and can contribute to many practical applications,such as detecting the abnormal structures of human brain networks.