Related papers: Morse Index Classification and Landscape of Kuramo…
This paper explores the fundamental limits of a simple system, inspired by the intermittent Kalman filtering model, where the actuation direction is drawn uniformly from the unit hypersphere. The model allows us to focus on a fundamental…
Many high-dimensional complex systems exhibit an enormously complex landscape of possible asymptotic states. Here, we present a numerical approach geared towards analyzing such systems. It is situated between the classical analysis with…
The state-of-the art machine learning approach to training deep neural networks, backpropagation, is implausible for real neural networks: neurons need to know their outgoing weights; training alternates between a bottom-up forward pass…
There are a number of models of coupled oscillator networks where the question of the stability of fixed points reduces to calculating the index of a graph Laplacian. Some examples of such models include the Kuramoto and Kuramoto--Sakaguchi…
A new approach is introduced to classify faults in rotating machinery based on the total energy signature estimated from sensor measurements. The overall goal is to go beyond using black-box models and incorporate additional physical…
Kuramoto's differential equation describes a synchronization process between several harmonic oscillators. It has been used to model biological phenomena such as the synchronization of heart cells, the circadian rhythm, or brain waves. It…
M. Kruskal showed that each nearly-periodic dynamical system admits a formal $U(1)$ symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly-invariant manifolds of each order, near which rapid…
Navigating in off-road environments for wheeled mobile robots is challenging due to dynamic and rugged terrain. Traditional physics-based stability metrics, such as Static Stability Margin (SSM) or Zero Moment Point (ZMP) require knowledge…
Visual-inertial systems rely on precise calibrations of both camera intrinsics and inter-sensor extrinsics, which typically require manually performing complex motions in front of a calibration target. In this work we present a novel…
We study the numerical stability of the Sherman-Morrison-Woodbury (SMW) identity. Let $B = A + UV^T$ and assume $U$ and $V$ both have full-column rank. We explore error bounds for the SMW identity when we are only able to compute…
This article is intended to present a qualitative and numerical analysis of well-posedness and boundary stabilization problems of the well-known Korteweg-de Vries-Burgers equation. Assuming that the boundary control is of memory type, the…
The primate brain contains a hierarchy of visual areas, dubbed the ventral stream, which rapidly computes object representations that are both specific for object identity and relatively robust against identity-preserving transformations…
In this work, we study the inertial Kuramoto model, which is a second-order extension of the classical first-order Kuramoto model, as an inertial perturbation of the first-order Kuramoto model. We develop a quantitative Tikhonov theorem,…
While excitonic instabilities in multiorbital systems recently have come under scrutiny in a variety of transition-metal compounds, understanding emergence of these instabilities from strong electronic interactions has remained a challenge.…
In this paper we develop further a method for detecting unstable periodic orbits (UPOs) by stabilising transformations, where the strategy is to transform the system of interest in such a way that the orbits become stable. The main…
The Kuramoto model describes a system of globally coupled phase-only oscillators with distributed natural frequencies. The model in the steady state exhibits a phase transition as a function of the coupling strength, between a low-coupling…
This paper focuses on using curvature and torsion to describe the stability of linear time-invariant system. We prove that for a two-dimensional system $\dot{r}(t)= Ar(t)$, (i) if there exists an initial value, such that zero is not the…
We consider the classical Kuramoto model (KM) with natural frequencies and its continuum limit (CL), and discuss the existence of synchronized solutions and their bifurcations and stability. We specifically assume that the frequency…
In the outer solar system, the Kuiper Belt contains dynamical sub-populations sculpted by a combination of planet formation and migration and gravitational perturbations from the present-day giant planet configuration. The subdivision of…
We investigate the connection between the dynamics of synchronization and the modularity on complex networks. Simulating the Kuramoto's model in complex networks we determine patterns of meta-stability and calculate the modularity of the…