45 citations · 88 across the 10 of their papers we have counts for
11 papers
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…
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.,…
Spectral Submanifolds of the Navier-Stokes Equations
Gergely Buza
Spectral subspaces of a linear dynamical system identify a large class of invariant structures that highlight/isolate the dynamics associated to select subsets of the spectrum. The…
Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number
Gergely Buza, Miguel Beneitez, Jacob Page +1
Using branch continuation in the FENE-P model, we show that finite-amplitude travelling waves borne out of the recently-discovered linear instability of viscoelastic channel flow (…
Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers
Gergely Buza, Jacob Page, Rich R. Kerswell
The recently-discovered centre-mode instability of rectilinear viscoelastic shear flow (Garg et al. Phy. Rev. Lett. 121, 024502, 2018) has offered an explanation for the origin of…
Integral Equations & Model Reduction For Fast Computation of Nonlinear Periodic Response
Gergely Buza, George Haller, Shobhit Jain
We propose a reformulation for the integral equations approach of Jain, Breunung \& Haller [Nonlinear Dyn. 97, 313--341 (2019)] to steady-state response computation for periodicall…
Using Spectral Submanifolds for Optimal Mode Selection in Model Reduction
Gergely Buza, Shobhit Jain, George Haller
Model reduction of large nonlinear systems often involves the projection of the governing equations onto linear subspaces spanned by carefully-selected modes. The criteria to selec…