Related papers: Spatio-temporal patterns driven by autocatalytic i…
Self-organization through noisy interactions is ubiquitous across physics, mathematics, and machine learning, yet how long-range structure emerges from local noisy dynamics remains poorly understood. Here, we investigate three paradigmatic…
Traditional chemical kinetics may be inappropriate to describe chemical reactions in micro-domains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a…
A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the…
The position of a reaction front, propagating into a metastable state, fluctuates because of the shot noise of reactions and diffusion. A recent theory [B. Meerson, P.V. Sasorov, and Y. Kaplan, Phys. Rev. E 84, 011147 (2011)] gave a closed…
We show the relation between processes which are modeled by a Langevin equation with multiplicative noise and infinite ergodic theory. We concentrate on a spatially dependent diffusion coefficient that behaves as ${D(x)}\sim…
We analyze the effects of additive, spatially extended noise on spatiotemporal patterns in continuum neural fields. Our main focus is how fluctuations impact patterns when they are weakly coupled to an external stimulus or another…
Noise is often used in the study of open systems, such as in classical Brownian motion and in Quantum Dynamics, to model the influence of the environment. However generalising results from G\"{o}del and Chaitin in mathematics suggests that…
Brownian yet non-Gaussian processes have recently been observed in numerous biological systems and the corresponding theories have been built based on random diffusivity models. Considering the particularity of random diffusivity, this…
We consider the response of a dynamical system driven by external adiabatic fluctuations. Based on the `adiabatic following approximation' we have made a systematic separation of time-scales to carry out an expansion in $\alpha |\mu|^{-1}$,…
We demonstrate that demographic noise can induce persistent spatial pattern formation and temporal oscillations in the Levin-Segel predator-prey model for plankton-herbivore population dynamics. Although the model exhibits a Turing…
External fluctuations have a wide variety of constructive effects on the dynamical behavior of spatially extended systems, as described by stochastic partial differential equations. A set of paradigmatic situations exhibiting such effects…
We characterize the influence that external noise, with both spatial and temporal correlations, has on the scale dependence of the reaction parameters of a cubic autocatalytic reaction diffusion (CARD) system. Interpreting the CARD model as…
Studies about the constructive aspects of noise and fluctuations in different non-linear systems have shown that the addition of external noise to systems with an intrinsic noise may result in a less noisy response. Recently, the…
Theoretical and experimental studies have shown that the fluctuations of in vivo systems break the fluctuation-dissipation theorem. One can thus ask what information is contained in the correlation functions of protein concentrations and…
We use macroscopic fluctuation theory (MFT) to analyse current fluctuations in a non-interacting Brownian gas with one or more partially absorbing targets within a bounded domain $\Omega \subset \R^d$. We proceed by coarse-graining a…
I show stable, localized, single and multi-spot patterns of three classes - stationary, moving, and rotating - that exist within a limited range of parameter values in the two-dimensional Gray-Scott reaction-diffusion model with ${\sigma} =…
We consider the long-time dynamics of a general class of nonlinear Fokker-Planck equations, describing the large population behavior of mean-field interacting units. The main motivation of this work concerns the case where the individual…
In this manuscript we analyze the collective behavior of mean-field limits of large-scale, spatially extended stochastic neuronal networks with delays. Rigorously, the asymptotic regime of such systems is characterized by a very intricate…
The counterintuitive emergence of order from noise is a central phenomenon in science, ranging from pattern formation and synchronization to order-by-disorder in frustrated systems. While large-scale spatial self-organization induced by…
Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived. Use is made of the fact that for this problem…