Extension to non-identical units and beyond identical synchronisation

Extend the equitability-based characterisation of cluster synchronisation and the quotient-dynamics framework from identical dynamical units to systems of non-identical dynamical units in general multilayer networks, and to synchronisation types beyond identical synchronisation.

Background

All results in the paper assume identical units and focus on identical (cluster) synchronisation. Real systems often exhibit parameter heterogeneity and display other synchronisation forms (e.g., phase or generalized synchronisation).

The authors explicitly identify the need to broaden the current theory to heterogeneous units and to synchronisation phenomena beyond identical synchronisation in multilayer settings.