  Various disasters stem from minor perturbations, such as the spread of
infectious diseases, cascading failure in power grids, etc. Analyzing
perturbations is crucial for both theoretical and application fields. Previous
researchers have proposed basic propagation patterns for perturbation and
explored the impact of basic network motifs on the collective response to these
perturbations, However, the current framework is limited in its ability to
decouple interactions, and therefore cannot analyze more complex structures. In
this article, we establish an effective, robust and powerful propagation
framework under a general dynamic model. This framework reveals common and
dense network motifs that exert a critical influence on signal propagation,
often spanning orders of magnitude compared with conclusions generated by
previous work. Moreover, our framework provides a new approach to understand
the fundamental principles of complex systems and the negative feedback
mechanism, which is of great significance for research of system controlling
and network resilience.
