Related papers: A random dynamical systems perspective on stochast…
We study the random attractors associated with the stochastic fractional Schr\"odinger equation on $\mathbb{R}^n$. Utilizing the stochastic Strichartz estimates for the damped fractional Schr\"odinger equation with Gaussian noise, we show…
As circuits continue to miniaturize, noise has become a significant obstacle to performance optimization. Stochastic resonance in logic circuits offers an innovative approach to harness noise constructively; however, current implementations…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to…
We consider a 2-dimensional stochastic differential equation in polar coordinates depending on several parameters. We show that if these parameters belong to a specific regime then the deterministic system explodes in finite time, but the…
Along with the development of interferometric gravitational wave detector, we enter into an epoch of gravitational wave astronomy, which will open a brand new window for astrophysics to observe our universe. Almost all of the data analysis…
The problem of a linear damped noisy oscillator is treated in the presence of two multiplicative sources of noise which imply a random mass and random damping. The additive noise and the noise in the damping are responsible for an influx of…
Here we present a simple stochastic threshold model consisting of a deterministic slowly decaying term and a fast stochastic noise term. The process shows a pseudo-resonance, in the sense that for small and large intensities of the noise…
We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect-product extension. Random…
Systems in nature are stochastic as well as nonlinear. In traditional applications, engineered filters aim to minimize the stochastic effects caused by process and measurement noise. Conversely, a previous study showed that the process…
In this paper, we consider the 2D periodic stochastic Nernst-Planck-Navier-Stokes equations with body forces perturbed by multiplicative white noise. We first transform the stochastic Nernst-Planck-Navier-Stokes system into the…
The dynamics of a system formed by a finite number $N$ of globally coupled bistable oscillators and driven by external forces is studied focusing on a global variable defined as the arithmetic mean of each oscillator variable. Several…
We show that a dispersion of monodomain ferromagnetic particles in a solid phase exhibits stochastic resonance when a driven linearly polarized magnetic field is applied. By using an adiabatic approach, we calculate the power spectrum, the…
We investigate instabilities in a stochastic mathematical model of cochlear dynamics. The cochlea is modeled as a spatio-temporal dynamical system made up of a spatially distributed array of coupled oscillators, together with the cochlear…
Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order…
We investigate the dynamics of a soliton that behaves as an extended particle. The soliton motion in an effective bistable potential can be chaotic in a similar way as the Duffing oscillator. We generalize the concept of geometrical…
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…
The combination of a strong pump and a weak probe has been widely applied to investigate both optical and nanomechanical devices. Such pump-probe measurements allows for the exploration of nonlinear dynamics, driven by the large pump tone,…
When two systems are coupled, the driver system can function as an external forcing over the driven or response system. Also, an external forcing can independently perturb the driven system, leading us to examine the interplay between the…
We consider an overdamped Brownian motion in "quartic" potential subjected to periodic driving. This system for the case of a weak periodic driving has been intensively studied during past decade within the context of stochastic resonance.…