Related papers: Discriminating dynamical from additive noise in th…

We study detection methods for multivariable signals under dependent noise. The main focus is on three-dimensional signals, i.e. on signals in the space-time domain. Examples for such signals are multifaceted. They include geographic and…

In this paper, we address the problem of modeling data with periodic autoregressive (PAR) time series and additive noise. In most cases, the data are processed assuming a noise-free model (i.e., without additive noise), which is not a…

Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…

Stochastic differential equations describe well many physical, biological and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and…

We study analytically and numerically the problem of a nonlinear mechanical oscillator with additive noise in the absence of damping. We show that the amplitude, the velocity and the energy of the oscillator grow algebraically with time.…

In this work, we present the basic theoretical efforts that are known in order to deal with non-trivial solutions of the Van der Pol oscillator, such as theory of average, successive approximations and symbolic dynamics. We also construct a…

We show that the dipole, a system usually proposed to model relaxation phenomena, exhibits a maximum in the signal-to-noise ratio at a non-zero noise level, thus indicating the appearance of stochastic resonance. The phenomenon occurs in…

This paper is concerned with the problem of recovering a finite, deterministic time series from observations that are corrupted by additive, independent noise. A distinctive feature of this problem is that the available data exhibit…

We have analyzed the interplay between noise and periodic modulations in a mean field model of a neural excitable medium. To this purpose, we have considered two types of modulations; namely, variations of the resistance and oscillations of…

In order to evaluate and compare different recursive filters, simulation is a common tool and numerous simulation models are widely used as 'benchmark'. In the simulation, the continuous time dynamic system is converted into a discrete-time…

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…

In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…

This study focuses on extending the concept of weak signal enhancement from dynamical systems based on vibrational resonance of nonlinear systems, to non-smooth systems. A Van der Pol- Duffing oscillator with a one-sided barrier, subjected…

The study of multiplicative noise models has a long history in control theory but is re-emerging in the context of complex networked systems and systems with learning-based control. We consider linear system identification with…

It is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise. Here we present a general operational method to extract measurement noise from stochastic time…

Noisy dynamical models are employed to describe a wide range of phenomena. Since exact modeling of these phenomena requires access to their microscopic dynamics, whose time scales are typically much shorter than the observable time scales,…

The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data. An algorithm based on the least-squares method and multiple-trajectory data is proposed for joint estimation of the nominal system…

The leading workhorse of anomaly (and attack) detection in the literature has been residual-based detectors, where the residual is the discrepancy between the observed output provided by the sensors (inclusive of any tampering along the…

We study the evolution of observables of dynamical systems. For linear systems, we show that observables satisfy a closed differential equation whose minimal order is determined by the dynamical system and observation operator. This yields…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…