Related papers: A noise-controlled dynamic bifurcation
The issue of white-noise-aided control is considered and its availability is proved. And a noise-aiding way is developed to stabilize perturbed systems to be input-to-state stable (ISS) with respect to (w.r.t.) perturbations. To illustrate…
A discretization of an optimal control problem of a stochastic parabolic equation driven by multiplicative noise is analyzed. The state equation is discretized by the continuous piecewise linear element method in space and by the backward…
We study the effect of extrinsic noise in metabolic networks. We introduce external random fluctuations at the kinetic level, and show how these lead to a stochastic generalization of standard Metabolic Control Analysis. While Summation and…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…
In this paper, we consider asymptotic behaviors of multiscale multivalued stochastic systems with small noises. First of all, for general, fully coupled systems for multivalued stochastic differential equations of slow and fast motions with…
The effect of stochasticity, in the form of Gaussian white noise, in a predator-prey model with two distinct time-scales is presented. A supercritical singular Hopf bifurcation yields a Type II excitability in the deterministic model. We…
We propose a novel data-driven stochastic model predictive control framework for uncertain linear systems with noisy output measurements. Our approach leverages multi-step predictors to efficiently propagate uncertainty, ensuring chance…
Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and…
Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…
We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest…
Populations of globally coupled identical maps subject to additive, independent noise are studied in the regimes of strong coupling. Contrary to each noisy population element, the mean field dynamics undergoes qualitative changes when the…
The long term aim is to use modern dynamical systems theory to derive discretisations of noisy, dissipative partial differential equations. As a first step we here consider a small domain and apply stochastic centre manifold techniques to…
We study stochastic bifurcation for a system under multiplicative stable Levy noise (an important class of non-Gaussian noise), by examining the qualitative changes of equilibrium states in its most probable phase portraits. We have found…
We provide an example for stabilization by noise. Our approach does not rely on monotonicity arguments due to the presence of higher order differential operators or mixing properties of the system as the noise might be highly degenerate. In…
In this paper, we study the dynamics of a linear control system with given state feedback control law in the presence of fast periodic sampling at temporal frequency $1/\delta$ ($0 < \delta \ll 1$), together with small white noise…
We study the distribution of maxima (Extreme Value Statistics) for sequences of observables computed along orbits generated by random transformations. The underlying, deterministic, dynamical system can be regular or chaotic. In the former…
Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…
The objectives and contributions of this paper are mathematical and numerical analyses of a stochastic control problem of bounded population dynamics under ambiguity, an important but not well-studied problem, focusing on the optimality…
We show a noise-induced transition in Josephson junction with fundamental as well as second harmonic. A periodically modulated multiplicative colored noise can stabilize an unstable configuration in such a system. The stabilization of the…