Related papers: Local stability analysis of differential equations…

This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to…

Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid…

This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization…

In this paper we consider the global stability of solutions of an affine stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…

This paper is concerned with establishing global asymptotic stability results for a class of non-linear PDE which have some similarity to the PDE of the Lifschitz-Slyozov-Wagner model. The method of proof does not involve a Lyapounov…

We consider linear delay differential equations at the verge of Hopf instability, i.e. a pair of roots of the characteristic equation are on the imaginary axis of the complex plane and all other roots have negative real parts. When…

A Lyapunov-Krasovskii functional with prescribed derivative whose construction does not require the stability of the system is introduced. It leads to the presentation of stability/instability theorems. By evaluating the functional at…

This paper is devoted to the study of tilt stability in finite dimensional optimization via the approach of using the subgradient graphical derivative. We establish a new characterization of tilt-stable local minimizers for a broad class of…

Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When…

We study a one-dimensional nonlinear Vlasov equation with a local self-consistent force field generated by the density, where the force is given by the spatial derivative of a real-analytic nonlinearity. For small analytic initial data, we…

Railway tracks rest on a foundation known for exhibiting nonlinear viscoelastic behavior. Railway track deflections are modeled by a semilinear partial differential equation. This paper studies the stability of solutions to this equation in…

This paper presents a novel framework for stabilizing nonlinear systems represented in state-dependent form. We first reformulate the nonlinear dynamics as a state-dependent parameter-varying model and synthesize a stabilizing controller…

It is well-known that the exponential stability of Integral Difference Equations and Delay Difference Equations, in the usual state space of continuous functions, is equivalent to the location of the roots of its associated characteristic…

The purpose of this paper is to investigate the stabilization of a one-dimensional coupled wave equations with non smooth localized viscoelastic damping of Kelvin-Voigt type and localized time delay. Using a general criteria of…

This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…

This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…

Motivated by the ubiquitous sampled-data setup in applied control, we examine the stability of a class of difference equations that arises by sampling a right- or left-invariant flow on a matrix Lie group. The map defining such a difference…

Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant…

In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…

Tilt stability is a fundamental concept of variational analysis and optimization that plays a pivotal role in both theoretical issues and numerical computations. This paper investigates tilt stability of local minimizers for a general class…