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We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as Ornstein-Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite…

Statistical Mechanics · Physics 2026-04-14 Dongho Lee , Jae-Hyung Jeon , Pascal Viot , Gleb Oshanin

Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative…

Populations and Evolution · Quantitative Biology 2017-02-16 Ivo Siekmann , Michael Bengfort , Horst Malchow

We introduce an approach for analyzing the responses of dynamical systems to external perturbations that combines score-based generative modeling with the Generalized Fluctuation-Dissipation Theorem (GFDT). The methodology enables accurate…

Data Analysis, Statistics and Probability · Physics 2024-11-11 Ludovico Theo Giorgini , Katherine Deck , Tobias Bischoff , Andre Souza

We show the existence of internal stochastic resonance in a microscopic stochastic model for the oscillating CO oxidation on single crystal surfaces. This stochastic resonance arises directly from the elementary reaction steps of the system…

Condensed Matter · Physics 2007-05-23 O. Kortlüke , V. N. Kuzovkov , W. von Niessen

We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common…

Probability · Mathematics 2025-10-21 Razvan C. Fetecau , Hui Huang , Jinniao Qiu

The dynamics and stability of multi-spot patterns to the Gray-Scott (GS) reaction-diffusion model in a two-dimensional domain is studied in the singularly perturbed limit of small diffusivity $\epsilon$ of one of the two solution…

Pattern Formation and Solitons · Physics 2010-09-16 Wan Chen , Michael J. Ward

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the…

Statistical Mechanics · Physics 2009-11-07 A. Rocco , L. Ramirez-Piscina , J. Casademunt

We explore the joint effect of the intrinsic noise and time delay on the spatial pattern formation within a multi-scale mobile lattice model of the epithelium. The protein fluctuations are driven by transcription/translation processes in…

Adaptation and Self-Organizing Systems · Physics 2015-06-12 Dmitry Bratsun , Andrey Zakharov

We formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within…

Statistical Mechanics · Physics 2015-12-18 L. Bertini , A. De Sole , D. Gabrielli , G. Jona-Lasinio , C. Landim

We generalize the oscillator model of a particle interacting with a thermal reservoir by introducing arbitrary nonlinear couplings in the particle coordinates.The equilibrium positions of the heat bath oscillators are promoted to space-time…

High Energy Physics - Theory · Physics 2009-10-28 F. Illuminati , M. Patriarca , P. Sodano

We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can…

Statistical Mechanics · Physics 2022-01-28 Davide Breoni , Ralf Blossey , Hartmut Löwen

In spatially distributed cellular systems, it is often convenient to represent complicated auxiliary pathways and spatial transport by time-delayed reaction rates. Furthermore, many of the reactants appear in low numbers necessitating a…

Quantitative Methods · Quantitative Biology 2015-05-14 Matthew Scott

We propose a new non-equilibrium model for spatial pattern formation on the basis of local information transfer. Unlike standard models of pattern formation it is not based on the Turing instability. Information is transmitted through the…

Statistical Mechanics · Physics 2007-05-23 Thimo Rohlf , Stefan Bornholdt

Starting from our recent chemical master equation derivation of the model of an autocatalytic reaction-diffusion chemical system with reactions $U+2V {\stackrel {\lambda_0}{\rightarrow}}~ 3 V;$ and $V {\stackrel {\mu}{\rightarrow}}~P$, $U…

Statistical Mechanics · Physics 2014-06-24 Fred Cooper , Gourab Ghoshal , Juan Pérez-Mercader

The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of…

Statistical Mechanics · Physics 2017-01-11 Tommaso Biancalani , Farshid Jafarpour , Nigel Goldenfeld

We present a new approach to the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field,…

Statistical Mechanics · Physics 2009-11-11 Alexei Andreanov , Giulio Biroli , Jean-Philippe Bouchaud , Alexandre Lefevre

Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and analyzes a class of stochastic reaction-diffusion partial differential equations. In contrast to the models in the literature, the new formulation…

Probability · Mathematics 2021-05-10 N. N. Nguyen , G. Yin

Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…

Statistical Mechanics · Physics 2019-05-29 Joseph W. Baron , Tobias Galla

Numerical studies of the May-Leonard model for cyclically competing species exhibit spontaneous spatial structures in the form of spirals. It is desirable to obtain a simple coarse-grained evolution equation describing spatio-temporal…

Statistical Mechanics · Physics 2017-09-08 Shannon R. Serrao , Uwe C. Täuber

Starting from the chemical master equation, we employ field theoretic techniques to derive Langevin-type equations that exactly describe the stochastic dynamics of the Frank chiral amplification model with spatial diffusion. The intrinsic…

Populations and Evolution · Quantitative Biology 2007-05-23 David Hochberg , Maria-Paz Zorzano