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Phase transitions and effects of external noise on many body systems are one of the main topics in physics. In mean field coupled nonlinear dynamical stochastic systems driven by Brownian noise, various types of phase transitions including…

Statistical Mechanics · Physics 2015-05-13 Akihisa Ichiki , Masatoshi Shiino

Despite the celebrated success of stochastic control approaches for uncertain systems, such approaches are limited in the ability to handle non-Gaussian uncertainties. This work presents an adaptive robust control for linear uncertain…

Optimization and Control · Mathematics 2026-01-13 Xuehui Ma , Shiliang Zhang , Zhiyong Sun , Xiaohui Zhang , Sabita Maharjan

Assessing data informativity, determining whether the measured data contains sufficient information for a specific control objective, is a fundamental challenge in data-driven control. In noisy scenarios, existing studies deal with system…

Optimization and Control · Mathematics 2026-04-02 Taira Kaminaga , Hampei Sasahara

Large populations of globally-coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that for strong coupling, the collective…

Statistical Mechanics · Physics 2009-11-10 Silvia De Monte , Francesco d'Ovidio , Hugues Chaté , Erik Mosekilde

We study how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is persistence, it is usually impossible to say anything…

Populations and Evolution · Quantitative Biology 2025-07-15 Alexandru Hening , Siddharth Sabharwal

In this work we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic perturbations. For the linear case, we study robustness and existence of exponential dichotomies for nonautonomous…

Analysis of PDEs · Mathematics 2021-04-06 Tomás Caraballo , Alexandre N. de Carvalho , José A. Langa , Alexandre N. Oliveira-Sousa

The effect of small-amplitude noise on excitable systems with large time-scale separation is analyzed. It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle…

Quantitative Methods · Quantitative Biology 2007-05-23 Cyrill B. Muratov , Eric Vanden-Eijnden , Weinan E

This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for finite-time stability are presented via state…

Optimization and Control · Mathematics 2018-06-25 Tianliang Zhang , Feiqi Deng , Weihai Zhang

We study the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. While forward problems, such as existence, uniqueness, and regularity of the solution, for such equations…

Statistics Theory · Mathematics 2019-04-05 Igor Cialenco , Hyun-Jung Kim , Sergey V. Lototsky

Starting from the simple point process model of 1/f noise we derive a stochastic nonlinear differential equation for the signal exhibiting 1/f noise in any desirably wide range of frequency. A stochastic differential equation (the general…

Statistical Mechanics · Physics 2009-11-10 B. Kaulakys , J. Ruseckas

We study the dynamics of a simple adaptive system in the presence of noise and periodic damping. The system is composed by two paths connecting a source and a sink, the dynamics is governed by equations that usually describe food search of…

Statistical Mechanics · Physics 2021-12-23 Frederic Folz , Kurt Mehlhorn , Giovanna Morigi

Data-driven control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, besides measurement noise, stochastic disturbances might also directly affect…

Systems and Control · Electrical Eng. & Systems 2023-08-14 Guanru Pan , Ruchuan Ou , Timm Faulwasser

In this paper we show the existence and uniqueness of a solution for a stochastic differential equation driven by an additive noise which is the sum of two fractional Brownian motions with different Hurst parameters. The proofs are based on…

Probability · Mathematics 2022-07-12 David Nualart , Ercan Sönmez

The effects of noise on the dynamics of nonlinear systems is known to lead to many counter-intuitive behaviors. Using simple planar limit cycle oscillators, we show that the addition of moderate noise leads to qualitatively different…

Chaotic Dynamics · Physics 2015-06-17 Jay M. Newby , Michael A. Schwemmer

Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of…

The dichotomy between noise-stable and (completely) noise-sensitive stochastic models is of recent interest in probability theory. Of particular interest is the study of lattice models coming from statistical physics. The Fourier transform…

High Energy Physics - Theory · Physics 2007-05-23 Gil Kalai

Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…

Dynamical Systems · Mathematics 2025-06-24 Weiwei Qi , Zhongwei Shen , Yingfei Yi

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…

Chaotic Dynamics · Physics 2009-11-11 J. M. Finn , E. R. Tracy , W. E. Cooke , A. S. Richardson

We have analyzed the effects of the addition of external noise to non-dynamical systems displaying intrinsic noise, and established general conditions under which stochastic resonance appears. The criterion we have found may be applied to a…

Condensed Matter · Physics 2016-08-15 J. M. G. Vilar , G. Gomila , J. M. Rubí

The creation and subsequent evolution of marginally-unstable modes have been observed in a wide range of fusion devices. This behaviour has been successfully explained, for a single frequency shifting mode, in terms of phase-space…