Symmetry invariance in nonlinear dynamical complex networks

Abhijit Mondal, Subrata Ghosh, Prosenjit Kundu, Pitambar Khanra, Stefano Boccaletti, Pinaki Pal, Chittaranjan Hens

Research output: Contribution to journalArticlepeer-review


We delve into the interplay between network's symmetry and functioning for a generic class of dynamical systems. Primarily, we focus on a class of systems that characterize the spreading process, such as the spread of epidemics in complex networks, where the coupling configuration is nonlinear rather than diffusive. Through theoretical and numerical analysis, we establish a compelling connection between the symmetry of the graph and the trajectories followed by the dynamical processes for those nodes forming symmetry orbits and displaying identical eigenvector centrality. In particular, we are able to show that when the initial transitory states are removed, the symmetric group of nodes respond synchronously; nonetheless, they maintain a constant distance from each other and hence follow splay states. We have verified this phenomenon once more using two distinct kinds of networks. In one instance, every node takes part in nontrivial clusters. In the alternative scenario, we create symmetric orbits as per our target. The cluster nodes show splay states in both situations.

Original languageEnglish
Article number115002
JournalChaos, Solitons and Fractals
StatePublished - Aug 2024
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2024


  • Complex networks
  • Spreading
  • Symmetry


Dive into the research topics of 'Symmetry invariance in nonlinear dynamical complex networks'. Together they form a unique fingerprint.

Cite this