General principles governing multiplex topology–dynamics interplay

Establish the general organizing principles that govern the emergence of instabilities, hybrid phase transitions, metastability, and coexistence of dynamical regimes that arise from the interplay between multilayer topology and cross-layer dynamical coupling in multiplex networks, so as to determine when such phenomena occur and how they depend on structural and coupling parameters.

Background

The review highlights that multiplex architectures enable dynamical behaviors that do not appear in single-layer systems, including topology-induced instabilities, hybrid phase transitions, metastability, and coexistence of order and disorder. These phenomena stem from the interaction between multilayer topology and cross-layer dynamical coupling.

While many specific instances have been documented across domains, the authors emphasize the absence of a unifying set of principles that explains when and why such behaviors emerge, and how they depend on structure and coupling. They explicitly identify understanding these principles as a major open challenge for the field.

References

Understanding the general principles that govern these phenomena remains a major open challenge.

— Multilayer network science: theory, methods, and applications  (2511.23371 - Aleta et al., 28 Nov 2025) in Section "Outlook"

Whether this is a coincidence is an open question.

— Percolation on interdependent one-dimensional long-range networks  (2610.10097 - Sharabi et al., 7 Oct 2026) in Section Discussion, paragraph beginning “Perhaps the most interesting result”