相关论文: On the semi-dynamical reflection equation: solutio…
We study almost automorphic solutions of the discrete delayed neutral dynamic system% \[ x(t+1)=A(t)x(t)+\Delta Q(t,x(t-g(t)))+G(t,x(t),x(t-g(t))) \] by means of a fixed point theorem due to Krasnoselskii. Using discrete variant of…
We prove the existence and uniqueness of tempered random attractors for stochastic Reaction-Diffusion equations on unbounded domains with multiplicative noise and deterministic non-autonomous forcing. We establish the periodicity of the…
The main purpose of this work is to provide a non-local approach to study aspects of structural stability of 3D Filippov systems. We introduce a notion of semi-local structural stability which detects when a piecewise smooth vector field is…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…
The problem of linear instability of a nonlinear traveling wave in a canonical Hamiltonian system with translational symmetry subject to superharmonic perturbations is discussed. It is shown that exchange of stability occurs when energy is…
This paper establishes the well-posedness of stochastic partial differential equations with reflection in an infinite-dimensional ball, within the fully local monotone framework. Our result is very general, including many important models…
We investigate periodic integrable Markov models, constructed from set-theoretical solutions of the Yang-Baxter equation. We first focus on the simplest class of solutions, called Lyubashenko solutions. We show that the resulting models are…
This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a…
The seek for a new universal formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general…
Stable non-Gaussian self-similar mixed moving averages can be decomposed into several components. Two of these are the periodic and cyclic fractional stable motions which are the subject of this study. We focus on the structure of their…
We characterise asymptotic stability of port-Hamiltonian systems by means of matrix conditions using well-known resolvent criteria from $C_0$-semigroup theory. The idea of proof is based on a recent characterisation of exponential stability…
We investigate the stability of the wave equation with spatial dependent coefficients on a bounded multidimensional domain. The system is stabilized via a scattering passive feedback law. We formulate the wave equation in a port-Hamiltonian…
The modeling framework of port-Hamiltonian systems is systematically extended to constrained dynamical systems (descriptor systems, differential-algebraic equations). A new algebraically and geometrically defined system structure is…
The paper addresses the stabilization of nonlinear systems with semi-quadratic cost: quadratic with respect to controls and nonlinear for state variables. Paper presents the effective new feedback synthesis procedure. The novel feedback…
Sequences of parametrized Lyapunov equations can be encountered in many application settings. Moreover, solutions of such equations are often intermediate steps of an overall procedure whose main goal is the computation of…
A major result concerning perturbations of integrable Hamiltonian systems is given by Nekhoroshev estimates, which ensures exponential stability of all solutions provided the system is analytic and the integrable Hamiltonian not too…
The paper deals with the convergence properties of the products of random (row-)stochastic matrices. The limiting behavior of such products is studied from a dynamical system point of view. In particular, by appropriately defining a dynamic…
This paper concerns the existence of multiple rotating quasi-periodic solutions for second order Hamiltonian systems with sub-quadratic potential. Such solutions have the form $x(t+T)=Qx(t)$ for some orthogonal matrix $Q$. To deal with such…
We study the stability and dynamics of traveling-front solutions of a modified Kuramoto--Sivashinsky equation arising in the modeling of nanoscale ripple patterns that form when a nominally flat solid surface is bombarded with a broad ion…