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We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour…
We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic…
In recent years, there has been considerable interest in understanding the motion in Hamiltonian systems when phase space is divided into stochastic and integrable regions. This paper studies one aspect of this problem, namely, the motion…
Resonant activation is an effect of a noise-induced escape over a modulated potential barrier. The modulation of a energy landscape facilitates the escape kinetics and makes it optimal as measured by the mean first passage time. A canonical…
We study the generic problem of the escape of a classical particle over a fluctuating barrier under the influence of non-Gaussian noise mimicking the effects of not-fully equilibrated bath. Our attention focuses on the effect of the stable…
In laboratory studies and numerical simulations, we observe clear signatures of unstable time-periodic solutions in a moderately turbulent quasi-two-dimensional flow. We validate the dynamical relevance of such solutions by demonstrating…
Small islands in the vicinity of the mainland are believed to offer protection from wind and waves and thus coastal communities have been developed in these areas. However, what happens when it comes to tsunamis is not clear. Will these…
The Langevin equation for a particle (`random walker') moving in d-dimensional space under an attractive central force, and driven by a Gaussian white noise, is considered for the case of a power-law force, F(r) = - Ar^{-sigma}. The…
On the basis of input-output time-domain data collected from a complex simulator, this paper proposes a constructive methodology to infer a reduced-order linear, bilinear or quadratic time invariant dynamical model reproducing the…
We consider a general class of maps of the interval having Lyapunov subexponential instability $|\delta x_{t}|\sim|\delta x_{0}|\exp[\Lambda_{t}(x_{0})\zeta(t)]$, where $\zeta(t)$ grows sublinearly as $t\rightarrow\infty$. We outline here a…
We investigate the high dimensional Hamiltonian chaotic dynamics in $N$ coupled area-preserving maps. We show the existence of an enhanced trapping regime caused by trajectories performing a random walk {\em inside} the area corresponding…
A stability of nearly limiting Stokes waves to superharmonic perturbations is considered numerically. The new, previously inaccessible branches of superharmonic instability were investigated. Our numerical simulations suggest that…
Deep neural networks are extremely successful in various applications, however they exhibit high computational demands and energy consumption. This is exacerbated by stuttering technology scaling, prompting the need for novel approaches to…
The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems. We propose the use of an entropy-based measure of the recurrence plots (RP), namely, the entropy of the distribution of the recurrence times (estimated…
In theory, active control could be used to reduce the unwanted noise reflections from surfaces such as a submarine hull or the walls of an anechoic room. In the recent years, a real-time algorithm has been developed to this effect at the…
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…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…
The paper is concerned with a dissipativity theory and robust performance analysis of discrete-time stochastic systems driven by a statistically uncertain random noise. The uncertainty is quantified by the conditional relative entropy of…
Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed…
We are exploring two archetypal noise induced escape scenarios: escape from a finite interval and from the positive half-line under the action of the mixture of L\'evy and Gaussian white noises in the overdamped regime, for the random…