Related papers: Metastability of random maps: a resolvent approach
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
Robust and accurate calibration of macroscopic traffic flow models such as METANET is critical for reliable prediction and effective control. While gradient-based methods are desirable for high-dimensional parameter spaces, their…
In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This…
We continue development of the theory of Markov systems initiated in \cite{Wer1}. In this paper, we introduce fundamental Markov systems associated with random dynamical systems and show that the proof of the uniqueness and empiricalness of…
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…
We study the hitting times of Markov processes to target set $G$, starting from a reference configuration $x_0$ or its basin of attraction. The configuration $x_0$ can correspond to the bottom of a (meta)stable well, while the target $G$…
Metadynamics is a popular enhanced sampling scheme wherein by periodic application of a repulsive bias, one can surmount high free energy barriers and explore complex landscapes. Recently metadynamics was shown to be mathematically well…
We study metastability and nucleation in a kinetic two-dimensional Ising model which is driven out of equilibrium by a small random perturbation of the usual dynamics at temperature T. We show that, at a mesoscopic/cluster level, a…
Dynamic and evolving operational and economic environments present significant challenges for decision-making. We explore a simulation optimization problem characterized by non-stationary input distributions with regime-switching dynamics…
We study random perturbations of multidimensional piecewise expanding maps. We characterize absolutely continuous stationary measures (acsm) of randomly perturbed dynamical systems in terms of pseudo-orbits linking the ergodic components of…
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…
This work proposes a notion of robust reachability of one set from another set under constant control. This notion is used to construct a control strategy, involving sequential set-to-set reachability, which guarantees robust global…
We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under very general conditions on the interval maps and perturbation types, we prove strong stochastic…
We consider a general class of finite dimensional deterministic dynamical systems with finitely many local attractors $K^i$ each of which supports a unique ergodic probability measure $P^i$, which includes in particular the class of…
Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models…
We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of…
This paper proposes a robust disturbance observer framework for maritime autonomous surface vessels considering model and measurement uncertainties. The core contribution lies in a nonlinear disturbance observer, reconstructing the forces…
We study small random perturbations by additive white-noise of a spatial discretization of a reaction-diffusion equation with a stable equilibrium and solutions that blow up in finite time. We prove that the perturbed system blows up with…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…