Related papers: On decomposing mixed-mode oscillations and their r…
Model order reduction (MOR) has long been a mainstream strategy to accelerate large-scale transient circuit simulation. Dynamic Mode Decomposition (DMD) represents a novel data-driven characterization method, extracting dominant dynamical…
Wide-area synchrophasor ambient measurements provide a valuable data source for real-time oscillation mode monitoring and analysis. This paper introduces a novel method for identifying inter-area oscillation modes using wide-area ambient…
Traditional percolation theory assumes static microscopic rules, limiting its ability to describe real-world complex systems where macroscopic order actively regulates local interactions. Here, we introduce feedback percolation, an unified…
Scaling language models unlocks impressive capabilities, but the accompanying computational and memory demands make both training and deployment expensive. Existing efficiency efforts typically target either parameter sharing or adaptive…
In this paper, we use geometric singular perturbation theory and blowup, as our main technical tool, to study the mixed-mode oscillations (MMOs) that occur in two coupled FitzHugh-Nagumo units with symmetric and repulsive coupling. In…
Dynamic mechanical metamaterials (MMs) are artificial media composed of periodic micro-structures, designed to manipulate wave propagation. Modeling and designing these materials can be computationally demanding due to the broad design…
A recursive deformation of the boson commutation relation is introduced. Each step consists of a minimal deformation of a commutator $[a,\ad]=f_k(\cdots;\no)$ into $[a,\ad]_{q_{k+1}}=f_k(\cdots;\no)$, where $\cdots$ stands for the set of…
Singular Hopf bifurcation occurs in generic families of vector-fields with two slow variables and one fast variable. Normal forms for this bifurcation depend upon several parameters, and the dynamics displayed by the normal forms is…
Motivated by the dynamics of micro-scale oscillators with thermo-optical feedback, a simplified third order model, capturing the key features of these oscillators is developed, where each oscillator consists of a displacement variable…
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 study Mixed Mode Oscillations (MMOs) in systems of two weakly coupled slow/fast oscillators. We focus on the existence and properties of a folded singularity called FSN II that allows the emergence of MMOs in the presence of a suitable…
Quasicrystals (QCs) are a class of aperiodic ordered structures that emerge in various systems, from metallic alloys to soft matter and driven non-equilibrium systems. Within a mesoscale theory based on slowly-varying complex amplitudes for…
Spatially distributed limited-cycle oscillators are seen in various physical and biological systems. In internal organs, mechanical motions are induced by the stimuli of spatially distributed limit-cycle oscillators. We study several…
Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and…
A new method is presented for the analysis of limit cycle oscillations in mixed-feedback systems. The calculation of the limit cycle is reformulated as the zero finding of a mixed-monotone relation, that is, of the difference of two…
We analyze a piecewise-linear FitzHugh-Nagumo model. The system exhibits a canard near which both small amplitude and large amplitude periodic orbits exist. The addition of small noise induces mixed-mode oscillations (MMOs) in the vicinity…
There is an increasing interest in the amorphous states of metal-organic frameworks (MOFs) and porous coordination polymers, which can be produced by pressure-induced amorphization, temperature-induced amorphization, melt-quenching,…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
Modern applications increasingly involve many heterogeneous input streams, such as clinical sensors, wearable device data, imaging, and text, each with distinct measurement models, sampling rates, and noise characteristics. We define this…
We consider an inverse scattering problem for time-harmonic acoustic or electromagnetic waves. The goal is to localize several small penetrable objects embedded inside an otherwise homogeneous background medium from observations of far…