Related papers: A Stratum Approach to Global Stability of Complex …
The notion of stability can be generalised to point processes by defining the scaling operation in a randomised way: scaling a configuration by $t$ corresponds to letting such a configuration evolve according to a Markov branching particle…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
A wide body of work has applied the concept of critical slowing down to estimate the stability of different Earth system components. Most of them -- such as global vegetation -- are inherently non-stationary, for example due to strong…
It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…
In this letter we introduce a class of delayed kinetic systems derived from mass action type reaction network models. We define the time delayed positive stoichiometric compatibility classes and the notion of complex balanced time delayed…
This paper synthesizes anytime algorithms, in the form of continuous-time dynamical systems, to solve monotone variational inequalities. We introduce three algorithms that solve this problem: the projected monotone flow, the safe monotone…
Causally consistent distributed storage systems have received significant attention recently due to the potential for providing high throughput and causality guarantees. {\em Global stabilization} is a technique established for achieving…
The existence of a generalized fluctuation-dissipation theorem observed in simulations and experiments performed in various glassy materials is related to the concepts of local equilibration and heterogeneity in space. Assuming the…
The stability of ecological systems is a fundamental concept in ecology, which offers profound insights into species coexistence, biodiversity, and community persistence. In this article, we provide a systematic and comprehensive review on…
We consider a system of globally coupled rotors, described by a set of Langevin equations, and examine stability of the incoherent phase. The corresponding Fokker-Planck equation, providing a unified description of microcanonical and…
This article deals with the design of saturated controls in the context of partial differential equations. It focuses on a Korteweg-de Vries equation, which is a nonlinear mathematical model of waves on shallow water surfaces. Two different…
The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An…
In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and…
This paper provides a systematic exposition of Lyapunov stability for compact sets in locally compact metric spaces. We explore foundational concepts, including neighborhoods of compact sets, invariant sets, and the properties of dynamical…
The effects of the cosmological constant on the static equilibrium configurations and stability against small radial perturbations of relativistic polytropic spheres are investigated. This study numerically solves the hydrostatic…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
The aim of this paper is to introduce a class of Hamiltonian autonomous systems in dimension 4 which are completely integrable and their dynamics is described in all details. They have an equilibrium point which is stable for some rare…
We prove the stability of entropy solutions of nonlinear conservation laws with respect to perturbations of the initial datum, the space-time dependent flux and the entropy inequalities. Such a general stability theorem is motivated by the…
We study the stabilities of quantum states of macroscopic systems, against noises, against perturbations from environments, and against local measurements. We show that the stabilities are closely related to the cluster property, which…
Stability selection (Meinshausen and Buhlmann, 2010) makes any feature selection method more stable by returning only those features that are consistently selected across many subsamples. We prove (in what is, to our knowledge, the first…