Related papers: Coloured Noise from Stochastic Inflows in Reaction…
We prove existence and uniqueness of a reaction-diffusion equation whose diffusivity is a non-linear functional of the boundary temperature. We do this by studying systems of one-dimensional reflecting diffusions whose noise is a function…
Exploiting the information provided by the molecular noise of a biological process has proven to be valuable in extracting knowledge about the underlying kinetic parameters and sources of variability from single cell measurements. However,…
Regulation of intrinsic noise in gene expression is essential for many cellular functions. Correspondingly, there is considerable interest in understanding how different molecular mechanisms of gene expression impact variations in protein…
A recent study on the effect of colored driving noise on the escape from a metastable state derives an analytic expression of the transfer function of the leaky integrate-and-fire neuron model subject to colored noise. Here we present an…
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 system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to…
We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle. General expressions obtained are applied to the stochastic Lorenz system to show that departure from equilibrium…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
The ability to characterize the state of dynamic systems has been a pertinent task in the time series analysis community. Traditional measures such as Lyapunov exponents are often times difficult to recover from noisy data, especially if…
Diffusion models generate high-resolution images through iterative stochastic processes. In particular, the denoising method is one of the most popular approaches that predicts the noise in samples and denoises it at each time step. It has…
Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
Stochastic resonance (SR) is a coherence enhancement effect due to noise that occurs in periodically-driven nonlinear dynamical systems. A very broad range of physical and biological systems present this effect such as climate change,…
Many cellular behaviors are regulated by gene regulation networks, kinetics of which is one of the main subjects in the study of systems biology. Because of the low number molecules in these reacting systems, stochastic effects are…
Ecological, environmental and geophysical time series consistently exhibit the characteristics of coloured (1/f^\b{eta}) noise. Here we briefly survey the literature on coloured noise, population persistence and related evolutionary…
We consider the influence of stochastic perturbations on stability of a unique positive equilibrium of a difference equation subject to prediction-based control. These perturbations may be multiplicative $$x_{n+1}=f(x_n)-\left( \alpha +…
It is demonstrated, by means of analogue electronic simulation and theoretically, that external noise can markedly change the character of the response of a nonlinear system to a low-frequency periodic field. In general, noise of sufficient…
A system of coherently-driven two-level atoms is analyzed in presence of two independent stochastic perturbations: one due to collisions and a second one due to phase fluctuations of the driving field. The behaviour of the quantum…
Here we study a noise induced transition when the system is driven by a noise source taken as colored and non-Gaussian. We show--using both, a theoretical approximation and numerical simulations-- that there is a shift of the transition as…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…