Related papers: Unifying matrix stability concepts with a view to …
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
Dynamical systems, that are used to model power grids, the brain, and other physical systems, can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may…
This paper aims to initialize a dynamical aspect of symbolic integration by studying stability problems in differential fields. We present some basic properties of stable elementary functions and D-finite power series that enable us to…
This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the…
This paper addresses the ubiquity of remarkable measures on graphs, and their applications. In many queueing systems, it is necessary to take into account the compatibility constraints between users, or between supply and demands, and so…
We analyze the linear stability of monoclinal traveling waves on a constant incline, which connect uniform flowing regions of differing depths. The classical shallow-water equations are employed, subject to a general resistive drag term.…
Matrix stiffness expressions are derived for the particle movements in an assembly of rigid granules having compliant contacts. The derivations include stiffness terms that arise from the particle shapes at their contacts. These geometric…
Mackey-Glass equation arises in the leukemia model. We generalize this equation to include fractional-order derivatives in two directions. The first generalization contains one whereas the second contains two fractional derivatives. Such…
Stacking is a general approach for combining multiple models toward greater predictive accuracy. It has found various application across different domains, ensuing from its meta-learning nature. Our understanding, nevertheless, on how and…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
This paper investigates the stability of different regions in the $(k,\gamma)$-plane for a class of fractional delay differential equations given by \begin{equation} D^{\alpha} x(t) = -\gamma x(t) + g\big(x(t - \tau_1)\big) - e^{-\gamma…
We discuss how stability is related to the D-topology of mapping spaces, equipped with the functional diffeology. Indeed, we show that stable classes of mapping spaces are D-open. After a reformulation of the classical stability theorem of…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
In this paper, we are interested in investigating notions of stability for generalized linear differential equations (GLDEs). Initially, we propose and revisit several definitions of stability and provide a complete characterisation of them…
This paper continues the studies of symbolic integration by focusing on the stability problems on D-finite functions. We introduce the notion of stability index in order to investigate the order growth of the differential operators…
In this note, we discuss the extension of several important stable square matrices, e.g., D-stable matrices, diagonal dominance matrices, Volterra-Lyapunov stable matrices, to their corresponding non-square matrices. The extension is…
We develop a unified matrix-spectral framework for analyzing stability and interpretability in deep neural networks. Representing networks as data-dependent products of linear operators reveals spectral quantities governing sensitivity to…
A $d$-dimensional (bar-and-joint) framework $(G,p)$ consists of a graph $G=(V,E)$ and a realisation $p:V\to \mathbb{R}^d$. It is rigid if every continuous motion of the vertices which preserves the lengths of the edges is induced by an…
The differential equations involving two discrete delays are helpful in modeling two different processes in one model. We provide the stability and bifurcation analysis in the fractional order delay differential equation $D^\alpha x(t)=a…