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Dynamical systems (DS) theory is fundamental for many areas of science and engineering. It can provide deep insights into the behavior of systems evolving in time, as typically described by differential or recursive equations. A common…
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable…
This study employs scientific machine learning to identify transient time series of dynamical systems near a fold bifurcation of periodic solutions. The unique aspect of this work is that a convolutional neural network (CNN) is trained with…
The Koper model is a three-dimensional vector field that was developed to study complex electrochemical oscillations arising in a diffusion process. Koper and Gaspard described paradoxical dynamics in the model: they discovered complicated,…
Dry spinning is characterized by the simultaneous production of multiple thin polymeric fibers in airflows and the evaporation of the solvent contained in these fibers. This involves fiber-air interactions as well as radial diffusion…
We study fast-slow maps obtained by discretization of planar fast-slow systems in continuous time. We focus on describing the so-called delayed loss of stability induced by the slow passage through a singularity in fast-slow systems. This…
Coupled-wire description has been developed as a powerful framework for providing bosonic descriptions of strongly correlated quantum matter, with early applications to systems such as the cuprates and the integer and fractional quantum…
Following the paper of K. Shimizu et al. (2011) we consider the Bonhoeffer-van der Pol oscillator with non-autonomous periodic perturbation. We show that the presence of mixed mode oscillations reported in that paper can be explained using…
We investigate whether a strongly turbulent flow with intermittent large-scale reorganizations admits a compact state-space description. As a representative high-dimensional chaotic system we consider two-dimensional Rayleigh--B\'enard…
A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of…
We describe a transition from bursting to rapid spiking in a reduced mathematical model of a cerebellar Purkinje cell. We perform a slow-fast analysis of the system and find that -- after a saddle node bifurcation of limit cycles -- the…
Machine learning (ML) tools such as encoder-decoder convolutional neural networks (CNN) can represent incredibly complex nonlinear functions which map between combinations of images and scalars. For example, CNNs can be used to map…
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…
We propose sufficient conditions for existence of topologically stable periodic canard solutions in non-smooth slow-fast systems.
A data-driven method using Grassmann manifold learning is proposed to identify a low-dimensional actuation manifold for flow-controlled fluid flows. The snapshot flow field are twice compressed using Proper Orthogonal Decomposition (POD)…
We consider the problem of a slender rod slipping along a rough surface. Painlev\'e \cite{Painleve1895, Painleve1905a,Painleve1905b} showed that the governing rigid body equations for this problem can exhibit multiple solutions (the {\it…
The properties of constrained fluids have increasingly gained relevance for applications ranging from materials to biology. In this work, we propose a multiscale model using twin neural networks to investigate the properties of a fluid…
We present a machine learning (ML) force-field framework for simulating the non-equilibrium dynamics of charge-density-wave (CDW) order driven by the Peierls instability. Since the Peierls distortion arises from the coupling between lattice…
Hybrid systems, and especially piecewise affine (PWA) systems, are often used to model gene regulatory networks. In this paper we elaborate on previous work about control problems for this class of models, using also some recent results…
Nonlinear optical signals in optically driven quantum systems can reveal coherences and thereby open up the possibility for manipulation of quantum states. While the limiting cases of ultrafast and continuous-wave excitation have been…