Related papers: Ergodic Dynamics of the Stochastic Swift-Hohenberg…
We consider multiscale stochastic dynamical systems. In this article an \emph{intermediate} reduced model is obtained for a slow-fast system with fast mode driven by white noise. First, the reduced stochastic system on exponentially…
This paper compares the results of applying a recently developed method of stochastic uncertainty quantification designed for fluid dynamics to the Born-Infeld model of nonlinear electromagnetism. The similarities in the results are…
A Cahn-Hilliard equation with stochastic multiplicative noise and a random convection term is considered. The model describes isothermal phase-separation occurring in a moving fluid, and accounts for the randomness appearing at the…
Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative…
The influence of small random perturbations on a deterministic dynamical system with a locally stable equilibrium is considered. The perturbed system is described by the It\^{o} stochastic differential equation. It is assumed that the noise…
We show the appearance of spatiotemporal stochastic resonance in the Swift-Hohenberg equation. This phenomenon emerges when a control parameter varies periodically in time around the bifurcation point. By using general scaling arguments and…
Stochastic homogeneous hyperelastic solids are characterised by strain-energy densities where the parameters are random variables defined by probability density functions. These models allow for the propagation of uncertainties from input…
We suggest that the tools of contraction analysis for deterministic systems can be applied towards studying the convergence behavior of stochastic dynamical systems in the Wasserstein metric. In particular, we consider the case of Ito…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the…
The limiting stability of invariant probability measures of time homogeneous transition semigroups for autonomous stochastic systems has been extensively discussed in the literature. In this paper we initially initiate a program to study…
We utilize an ergodic theory framework to explore sublinear expectation theory. Specifically, we investigate the pointwise Birkhoff's ergodic theorem for invariant sublinear expectation systems. By further assuming that these sublinear…
In microscopic mechanical systems interactions between elastic structures are often mediated by the hydrodynamics of a solvent fluid. At microscopic scales the elastic structures are also subject to thermal fluctuations. Stochastic…
We consider a model describing a neuron and the input it receives from its dendritic tree when this input is a random perturbation of a periodic deterministic signal, driven by an Ornstein-Uhlenbeck process. The neuron itself is modeled by…
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…
Many physical and biological systems exhibit intrinsic cyclic dynamics that are altered by random external perturbations. We examine continuous-time autonomous dynamical systems exhibiting a stable limit cycle, perturbed by additive…
This work focuses on a class of stochastic Hamiltonian type jump diffusion systems with state-dependent switching, in which the switching component has countably infinite many states. First,the existence and uniqueness of the underlying…
An analytical theory, based on the perturbative treatment of the disorder and extended into a self-consistent set of equations for the dynamical density correlations, is developed and applied to the prototype one-dimensional model of…
The paper investigates the non-local property of quantum mechanics in the quantum hydrodynamic analogy (QHA) given by Madelung. The role of the quantum potential in generating the non-local dynamics of quantum mechanics is analyzed. The…
Stochastic versions of a classical model for natural ventilation are proposed and investigated to demonstrate the effect of random fluctuations on stability and predictability. In a stochastic context, the well-known deterministic result…