Related papers: A Contraction Theory Approach to Stochastic Increm…
In this paper, we revisit asymptotic stability for the two-dimensional incompressible porous media equation and the Stokes transport system in a periodic channel. It is well-known that a stratified density, which strictly decreases in the…
We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an…
Metastability in open system dynamics describes the phenomena of initial relaxation to longlived metastable states before decaying to the asymptotic stable states. It has been predicted in continuous-time stochastic dynamics of both…
We study the development of mean structures in a nonlinear model of large scale ocean dynamics with bottom topography and dissipation, and forced with a noise term. We show that the presence of noise in this nonlinear model leads to…
The convergence to the stationary regime is studied for Stochastic Differential Equations driven by an additive Gaussian noise and evolving in a semi-contractive environment, i.e. when the drift is only contractive out of a compact set but…
There is a whole range of emergent phenomena in non-equilibrium behaviors can be well described by a set of stochastic differential equations. Inspired by an insight gained during our study of robustness and stability in phage lambda…
In process operations, it is desirable to manage the sensitivity of the system output against external disturbance in the form of finite $\mathcal{L}_2$-gain stabilization. This matter is, however, nonsensical for stochastic systems because…
An attractor of a dynamical system may represent the system's 'desirable' state. Perturbations to the system may push the system out of the basin of attraction of the desirable attractor and into undesirable states. Hence, it is important…
The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of…
We develop a theory of static friction by modeling the homogeneous surfaces of contact as being composed of a regular array of compressible elastic smooth microscopic inclines. Static friction is thought of as the resistance due to having…
We study the effect of noise-enhanced stability of periodically driven metastable states in a system described by piecewise linear potential. We find that the growing of the average escape time with the intensity of the noise is depending…
We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…
Given a non-contracting trajectory of a nonlinear system, we consider the question of designing an input perturbation that makes the perturbed trajectory contracting. This paper stresses the analogy of this question with the classical…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…
A two dimensional flow model is introduced with deterministic behavior consisting of bursts which become successively larger, with longer interburst time intervals between them. The system is symmetric in one variable x and there are bursts…
It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of…
In this work, we present the stability theory for inhomogeneous fluids subjected to standing acoustic fields. Starting from the first principles, the stability criterion is established for two fluids of different acoustic impedance…
In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…
We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control…
Stochastic line integrals provide a useful tool for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled…