45 citations · 146 across the 16 of their papers we have counts for
17 papers
Data-driven modelling of autonomous and forced dynamical systems
Robert Szalai
The paper demonstrates that invariant foliations are accurate, data-efficient and practical tools for data-driven modelling of physical systems. Invariant foliations can be fitted…
Non-resonant invariant foliations of quasi-periodically forced systems
Robert Szalai
We show the existence and uniqueness of invariant foliations about invariant tori in analytic discrete-time dynamical systems. The parametrisation method is used prove the result.…
Machine-learning invariant foliations in forced systems for reduced order modelling
Robert Szalai
We identify reduced order models (ROM) of forced systems from data using invariant foliations. The forcing can be external, parametric, periodic or quasi-periodic. The process has…
Uncountably many cases of Filippov's sewed focus
Paul Glendinning, S. John Hogan, Martin Homer +2
The sewed focus is one of the singularities of planar piecewise smooth dynamical systems. Defined by Filippov in his book 'Differential Equations with Discontinuous Righthand Sides…
Measurements and linearized models for golf ball bounce
Stanisław W. Biber, Kristian M. Jones, Alan R. Champneys +2
A detailed set of experiments are described that capture over a 1000 different instances of the bounce of a golf ball. Video analysis is used to capture velocity and spin immediate…
Analysis of point-contact models of the bounce of a hard spinning ball on a compliant frictional surface
Stanisław W. Biber, Alan R. Champneys, Robert Szalai
Inspired by the turf-ball interaction in golf, this paper seeks to understand the bounce of a ball that can be modelled as a rigid sphere and the surface as supplying an elasto-pla…
Data-driven reduced order models using invariant foliations, manifolds and autoencoders
Robert Szalai
This paper explores how to identify a reduced order model (ROM) from a physical system. A ROM captures an invariant subset of the observed dynamics. We find that there are four way…
Invariant spectral foliations with applications to model order reduction and synthesis
Robert Szalai
The paper introduces a technique that decomposes the dynamics of a nonlinear system about an equilibrium into low order components, which then can be used to reconstruct the full d…
Conservative limit of two-dimensional spectral submanifolds
Robert Szalai
The paper is withdrawn. The proof has an error and it requires a different approach.
Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations
Robert Szalai, David Ehrhardt, George Haller
In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots…
Model reduction of non-densely defined piecewise-smooth systems in Banach spaces
Robert Szalai
In this paper a model reduction technique is introduced for piecewise-smooth (PWS) vector fields, whose trajectories fall into a Banach space, but the domain of definition of the v…
Nonlinear dynamics of the mammalian inner ear
Robert Szalai, Alan R. Champneys, Martin Homer
A simple nonlinear transmission-line model of the cochlea with longitudinal coupling is introduced that can reproduce Basilar membrane response and neural tuning in the chinchilla.…
Non-deterministic dynamics of a mechanical system
Robert Szalai, Mike R. Jeffrey
A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique…
Impact mechanics of elastic bodies with point contact
Robert Szalai
This paper introduces a modeling framework that is suitable to resolve singularities of impact phenomena encountered in applications. The method involves an exact transformation th…
Modelling elastic structures with strong nonlinearities with application to stick-slip friction
Robert Szalai
An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low dimensional equation with memor…
Decomposing the dynamics of heterogeneous delayed networks with applications to connected vehicle systems
Róbert Szalai, Gábor Orosz
Delay-coupled networks are investigated with nonidentical delay times and the effects of such heterogeneity on the emergent dynamics of complex systems are characterized. A simple…
Characteristic matrices for linear periodic delay differential equations
Jan Sieber, Robert Szalai
Szalai et al. (SIAM J. on Sci. Comp. 28(4), 2006) gave a general construction for characteristic matrices for systems of linear delay-differential equations with periodic coefficie…