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In this work we analyze the stochastic dynamics of the Kauffman model evolving under the influence of noise. By considering the average crossing time between two distinct trajectories, we show that different Kauffman models exhibit a…

This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…

This paper introduces a novel methodology for the identification of switching dynamics for switched autoregressive linear models. Switching behavior is assumed to follow a Markov model. The system's outputs are contaminated by possibly…

We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…

The paper deals with the problem of large-time behaviour of trajectories for discrete-time dynamical systems driven by a random noise. Assuming that the phase space is finite-dimensional and compact, and the noise is a Markov process with a…

We consider long-time behavior of dynamical systems perturbed by a small noise. Under certain conditions, a slow component of such a motion, which is most important for long- time evolution, can be described as a motion on the cone of…

We investigate the lifetime of dynamical regimes under the impact of noise motivated by low-dimensional models of the atmosphere. One may expect that the inclusion of noise tends to make the system leave prescribed regions of the state…

The aim of this paper is to study the dynamical behavior of non-autonomous stochastic lattice systems with Markovian switching. We first show existence of an evolution system of measures of the stochastic system. We then study the pullback…

It is a well established result that, in classical dynamical systems with sufficient time-scale separation, the fast chaotic degrees of freedom are well modeled by (Gaussian) white noise. In this paper, we present the stochastic dynamical…

A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…

The branching rule for the tower of wreath products of a finite group by the symmetric groups induces a stochastic process on the set of multiple Young diagrams through random transitions of boxes of the diagrams between one another. We…

The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…

Many learning algorithms can be represented as Markov processes, and understanding their generalization error is a central topic in learning theory. For specific continuous-time noisy algorithms, a prominent analysis technique relies on…

This paper concerns about the large time behavior of acoustic wave motion driven by a random force acting through the boundary. We begin with an abstract result showing the interconnection between the regularity of Markov semigroup…

Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…

There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often…

The work treats systems combining slow and fast motions depending on each other where fast motions are perturbations of families of either dynamical systems or Markov processes with freezed slow variable. In the first case we consider…

Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…

A continuous-time average consensus system is a linear dynamical system defined over a graph, where each node has its own state value that evolves according to a simultaneous linear differential equation. A node is allowed to interact with…

This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…