45 citations · 88 across the 10 of their papers we have counts for
4 papers · 1 filter
An application of the parameterization method to evolution flows associated to nonautonomous systems
Gergely Buza, George Haller
Let be a finite-dimensional complete Riemannian manifold of bounded geometry. We consider a time-dependent vector field with $X_t:=X(t,\cdot) \…
Spectral submanifold reduction for PDEs describing nonlinear continuum vibrations
Gergely Buza, George Haller
We prove the existence of spectral submanifolds in nonlinear partial differential equations (PDEs) describing forced-damped continuum vibrations. Our results cover structural vibra…
Data-Driven Reduced Modeling of Delayed Dynamical Systems via Spectral Submanifolds
Giacomo Abbasciano, Gergely Buza, George Haller
We show how the recent extension of spectral submanifold (SSM) theory to delay differential equations (DDEs) enables data-driven model reduction of nonlinear delay systems. First,…
Parametric Spectral Submanifolds across Hopf Bifurcations with Applications to Fluid Dynamics
James King, Bálint Kaszás, Gergely Buza +2
We investigate the persistence and regularity of spectral submanifolds (SSMs) in high-dimensional parametric dynamical systems undergoing a Hopf bifurcation. By analyzing how reson…