Related papers: Spatial Pattern Formation in External Noise: Theor…
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…
Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the…
We derivate the Langevin and the Fokker-Planck equations for the radius of $O(3)$-symmetric subcritical bubbles as a phenomenological model to treat thermal fluctuation. The effect of thermal noise on subcritical bubbles is examined. We…
Pattern formation in the classical and fractional Schnakenberg equations is studied to understand the nonlocal effects of anomalous diffusion. Starting with linear stability analysis, we find that if the activator and inhibitor have the…
In this paper, we present a spatial version of phytoplankton-zooplankton model that includes some important factors such as external periodic forces, noise, and diffusion processes. The spatially extended phytoplankton-zooplankton system is…
Models of diffusion driven pattern formation that rely on the Turing mechanism are utilized in many areas of science. However, many such models suffer from the defect of requiring fine tuning of parameters or an unrealistic separation of…
We present a picture of phase transitions of the system with colored multiplicative noise. Considering the noise amplitude as the power-law dependence of the stochastic variable $x^a$ we show the way to phase transitions disorder-order and…
We consider a system of independent point-like particles performing a Brownian motion while interacting with a Gaussian fluctuating background. These particles are in addition endowed with a discrete two-state internal degree of freedom…
The amplitude equation of Gierer-Mainhardt model has been actually derived near the boundary abuot which Turing and Hopf modes exist. In a parameter region where Hopf-Turing mixed mode solution is stable, a chaotic state that generally…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a…
In this paper we investigate the various aspects of noise and order in the micromaser system. In particular, we study the effect of adding fluctuations to the atom cavity transit time or to the atom-photon frequency detuning. By including…
We study the implications of quantum fluctuations of a dispersive medium, under steady rotation, either in or out of thermal equilibrium with its environment. A rotating object exhibits a quantum instability by dissipating its mechanical…
We develop a mean-field approach for multicomponent stochastic spatially extended systems and use it to obtain a multivariate nonlinear self-consistent Fokker-Planck equation defining the probability density of the state of the system,…
We theoretically and numerically investigate the spin fluctuations induced in a thermal atomic ensemble by an external fluctuating uniaxial magnetic field, in the context of a standard spin noise spectroscopy (SNS) experiment. We show that…
The author investigates the onset of patterns in vertically oscillated layers of dissipative particles using numerical solutions of continuum equations to Navier-Stokes order. Above a critical accelerational amplitude of the cell, standing…
Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of…
Perturbed Einstein's equations with a linear response relation and a stochastic source, applicable to a relativistic star model are worked out . These perturbations which are stochastic in nature, are of significance for building a…
A Langevin equation is suggested to describe a system driven by correlated Gaussian white noise as well as with positive and negative damping demarcated by a critical velocity. The equation can be transformed into the Fokker-Planck equation…
We consider the dynamics of pattern formation in a system of point defects under sustained irradiation within the framework of the rate theory. In our study we generalize the standard approach taking into account a production of defects by…