Special Session 136: Collective Dynamics in Large Networks: From Kuramoto to Spin Models

Adaptive and Higher-Order Dynamics of Kuramoto-type Models
Christian Kuehn
TUM
Germany
Co-Author(s):    
Abstract:
In my talk I shall provide a short survey of recent results I have obtained with a number of co-authors on considering Kuramoto-type models, where adaptive (or co-evolutionary) and higher-order (or polyadic) aspects play a key role. In particular, I shall discuss structural issues (e.g., how do simplicial and non-simplicical aspects form adaptively or arise via modelling), mean-field limits (on graph limits), as well as solutions to the resulting bifurcation problems. This highlights the importance of combining different mathematical approaches to understand Kuramoto-type models from first principles up to eventually understanding their complex dynamics.