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We consider the problem of computing the closest stable/unstable non-negative matrix to a given real matrix. This problem is important in the study of linear dynamical systems, numerical methods, etc. The distance between matrices is…

Dynamical Systems · Mathematics 2018-02-12 Nicola Guglielmi , Vladimir Yu. Protasov

We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…

Dynamical Systems · Mathematics 2017-05-16 Pawel Hitczenko , Georgi S. Medvedev

Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are…

Systems and Control · Computer Science 2017-04-11 Ian R. Manchester , Jean-Jacques E. Slotine

This work studies stability and robustness of a nonlinear system given as an interconnection of an ODE and a parabolic PDE subjected to external disturbances entering through the boundary conditions of the parabolic equation. To this end we…

Analysis of PDEs · Mathematics 2022-11-07 S. Dashkovskiy , O. Kapustyan , V. Slynko

The stability analysis of possibly time varying positive semigroups on non necessarily compact state spaces, including Neumann and Dirichlet boundary conditions is a notoriously difficult subject. These crucial questions arise in a variety…

Probability · Mathematics 2023-04-18 Marc Arnaudon , Pierre Del Moral , El Maati Ouhabaz

It is well known that ergodic theory can be used to formally prove a weak form of relaxation to equilibrium for finite, mixing, Hamiltonian systems. In this Letter we extend this proof to any dynamics that preserves a mixing equilibrium…

Statistical Mechanics · Physics 2018-12-18 Denis J. Evans , Stephen R. Williams , Lamberto Rondoni , Debra J. Searles

Due to their algorithmic simplicity and high accuracy, force-based model coupling techniques are an exciting development in computational physics. For example, the force-based quasicontinuum approximation is the only known pointwise…

Numerical Analysis · Mathematics 2015-05-13 Matthew Dobson , Mitchell Luskin , Christoph Ortner

We examine the stability of an Einstein-Maxwell perfect fluid configuration with a privileged direction of symmetry by means of a $1+1+2$-tetrad formalism. We use this formalism to cast, in a quasi linear symmetric hyperbolic form the…

High Energy Astrophysical Phenomena · Physics 2015-06-17 Daniela Pugliese , Juan A. Valiente Kroon

We show uniqueness and stability in $L^2$ and for all time for piecewise-smooth solutions to hyperbolic balance laws. We have in mind applications to gas dynamics, the isentropic Euler system and the full Euler system for a polytropic gas…

Analysis of PDEs · Mathematics 2020-11-26 Sam G. Krupa

In this paper, we establish the stability of the quasineutral limit for the ionic Vlasov-Poisson system under perturbations exponentially small in Wasserstein sense. Notably, we emphasize that exponential smallness is a necessary condition…

Analysis of PDEs · Mathematics 2024-03-08 Megan Griffin-Pickering , Mikaela Iacobelli

The robust statistical description of dynamical systems under perturbations is a central problem in ergodic theory. In this paper, we investigate the statistical properties of skew-product maps driven by a subshift of finite type with…

Dynamical Systems · Mathematics 2026-03-23 Davi Lima , Rafael Lucena

Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…

Dynamical Systems · Mathematics 2020-12-29 Mark A. Pinsky

We investigate two classes of non-minimally coupled curvature-matter models in the FLRW universe with a perfect fluid and analyze their cosmological implications using Supernova Ia, Observed Hubble Data, and Baryon Acoustic Oscillation…

General Relativity and Quantum Cosmology · Physics 2024-12-31 Anirban Chatterjee , Akshay Panda , Abhijit Bandyopadhyay

Three similar convergence notions are considered. Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions…

Optimization and Control · Mathematics 2018-11-06 Duc N. Tran , Björn S. Rüffer , Christopher M. Kellett

We determine the modulational stability of standing waves with small group velocity in quasi-onedimensional systems slightly above the threshold of a supercritical Hopf bifurcation. The stability limits are given by two different…

patt-sol · Physics 2009-09-25 Hermann Riecke , Lorenz Kramer

In this paper we present a switching control strategy to incrementally stabilize a class of nonlinear dynamical systems. Exploiting recent results on contraction analysis of switched Filippov systems derived using regularization, sufficient…

Systems and Control · Computer Science 2020-03-18 Mario di Bernardo , Davide Fiore

There appears to be a longtime, very slowly evolving state in dense simple fluids which, for high enough density, approaches a glassy nonergodic state. The nature of the nonergodic state can be characterized by the associated static…

Statistical Mechanics · Physics 2014-02-19 Gene F. Mazenko

We establish a relative energy framework for the Euler-Korteweg system with non-convex energy. This allows us to prove weak-strong uniqueness and to show convergence to a Cahn-Hilliard system in the large friction limit. We also use…

Analysis of PDEs · Mathematics 2017-09-08 Jan Giesselmann , Athanasios E. Tzavaras

We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…

Dynamical Systems · Mathematics 2015-11-05 Roland Bauerschmidt , David C. Brydges , Gordon Slade

This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or…

Systems and Control · Electrical Eng. & Systems 2024-05-13 Emily Jensen , Neelay Junnarkar , Murat Arcak , Xiaofan Wu , Suat Gumussoy