This research extends transfer operator theory in mean-field stochastic differential equations, revealing spectral properties and implications for dynamic systems.
Key Points
The study demonstrates how transfer operator theory can be extended to McKean-Vlasov equations, revealing complex dynamics.
Using dynamic mode decomposition, the study computes spectral properties for finite-dimensional approximations of transfer operators.
The findings indicate that this approach helps identify slowly evolving spatiotemporal patterns in complex systems.
Analyses were illustrated with benchmark models like the Cormier and Kuramoto models to validate the methodologies.