5 papers
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…
Existence of spectral submanifolds in time delay systems
Gergely Buza, George Haller
Spectral submanifolds (SSMs) are invariant manifolds of a dynamical system, defined by the property of being tangent to a spectral subspace of the linearized dynamics at a steady s…
Smooth invariant foliations and Koopman eigenfunctions about stable equilibria of semiflows
Gergely Buza
We consider a semiflow on a Banach space admitting a stable fixed point . We show, along the lines of the parameterization method (Cabré et al…