Abstract: The collective dynamics of man-made and natural complex systems represented by conventional graphs have long been modelled using pairwise networked Kuramoto phase oscillators. However, recently it has been realized that many real-world complex systems such as the Brain, society, ecology, etc have intrinsic higher-order interactions. In this talk, using the famous Kuramoto model, I will first show how incorporating higher-order interactions manifests emerging phenomena which is impossible if we only consider pair-wise interactions in the same system. Then, I will highlight the analytical challenges posed by higher-order interactions. In the end, I will provide potential applications for understanding the complex behaviour of the Brain and generating more robust power grids.
These are the few references of our recent works in this direction:
1. Tiered synchronization in adaptive Kuramoto oscillators on simplicial complexes
P Rajwani, A Suman, S Jalan, Chaos (Fast Track) Editors Choice Article (2023)
2. First-order route to antiphase clustering in adaptive simplicial complexes
AD Kachhvah, S Jalan, Physical Review E (Letter) 105 (6), L062203 (2022)
3. Hebbian plasticity rules abrupt desynchronization in pure simplicial complexes
AD Kachhvah, S Jalan, New Journal of Physics (Fast Track) 24, 052002 (2022)
4. Multiple first-order transitions in simplicial complexes on multilayer systems
S Jalan, A Suman, Physical Review E 106 (4), 044304 (2022)
Review article:
The structure and dynamics of networks with higher-order interactions
S Boccaletti, P De Lellis, CI del Genio, K Alfaro-Bittner, R Criado, S Jalan, M. Romance
Physics Reports 1018, 1-64 (2023)
