Related papers: Stochastic Turing patterns in the Brusselator mode…
Are spinodal instabilities the leading mechanism in the fragmentation of a fermionic system? Numerous experimental indications suggest such a scenario and stimulated much effort in giving a suitable description, without being finalised in a…
Fluctuations in small biological systems can be crucial for their function. Large-deviation theory characterizes such rare events from the perspective of stochastic processes. In most cases it is very difficult to directly determine the…
We propose a simple stochastic model of cascading transport in wave number space to clarify the origin of intermittent behavior of fully-developed fluid turbulence. In spite of lack of nonlinearity and viscosity the model gives non-Gaussian…
The classical fluctuation-dissipation theorem predicts the average response of a dynamical system to an external deterministic perturbation via time-lagged statistical correlation functions of the corresponding unperturbed system. In this…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
The emergence of stable disordered patterns in reactive system on spatially homogenous substrate is studied in the context of vegetation patterns in the semi-arid climatic zone. It is shown that reaction-diffusion systems that allow for…
The Brusselator reaction-diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the…
The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…
The emergence of localised radial patterns from a Turing instability has been well studied in two and three dimensional settings and predicted for higher spatial dimensions. We prove the existence of localised $(n+1)$-dimensional radial…
Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct features in terms of propagation speed and novel instabilities…
The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…
A stochastic subgrid-scale parameterization based on the Ruelle's response theory and proposed in Wouters and Lucarini [2012] is tested in the context of a low-order coupled ocean-atmosphere model for which a part of the atmospheric modes…
In a system of non-linear chemical reactions called the Brusselator, we show that {\it intrinsic noise} can be regulated to drive it to exhibit resonance in the presence of a sub-threshold signal. The phenomena of periodic stochastic…
Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Most theoretical approaches describe them as purely deterministic or stochastic dynamical…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
We analyze diffusion-driven (Turing) instability of a reaction-diffusion system. The innovation is that we replace the traditional Laplacian diffusion operator with a combination of the fourth order bi-Laplacian operator and the second…
Oscillations in a stochastic dynamical system, whose deterministic counterpart has a stable steady state, are a widely reported phenomenon. Traditional methods of finding parameter regimes for stochastically-driven resonances are, however,…
The stationary distribution of a fully chaotic system typically exhibits a fractal structure, which dramatically changes if the dynamical equations are even slightly modified. Perturbative techniques are not expected to work in this…
A particular type of random dynamical processes is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical…
This article is concerned with the time evolution of the oblique laminar-turbulent bands of transitional plane Couette flow under the influence of turbulent noise. Our study is focused on the amplitude of modulation of turbulence. In order…