Related papers: Isolating intrinsic noise sources in a stochastic …
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…
The intrinsic stochasticity of gene expression can lead to large variations in protein levels across a population of cells. To explain this variability, different sources of mRNA fluctuations ('Poisson' and 'Telegraph' processes) have been…
We present recent results on noise-induced transitions in a nonlinear oscillator with randomly modulated frequency. The presence of stochastic perturbations drastically alters the dynamical behaviour of the oscillator: noise can wash out a…
Gaussian boson sampling is an important protocol for testing the performance of photonic quantum simulators. As such, various noise sources have been investigated that degrade the operation of such devices. In this paper, we examine a…
A simple model of an irreversible process is introduced. The equation of iterations in the model includes a noise generation term. We study the properties of the system when the noise generation term is a stochastic process (e.g. a random…
We analyze a class of chemical reaction networks under mass-action kinetics and involving multiple time-scales, whose deterministic and stochastic models display qualitative differences. The networks are inspired by gene-regulatory…
Stochastic dynamics of chemical reactions in a mutually repressing two-gene circuit is numerically simulated. The circuit has a rich variety of different states when the kinetic change of DNA status is slow. The stochastic switching…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For…
Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed…
Transitions between multiple stable states of nonlinear systems are ubiquitous in physics, chemistry, and beyond. Two types of behaviors are usually seen as mutually exclusive: unpredictable noise-induced transitions and predictable…
We investigate the bifurcation phenomena for stochastic systems with multiplicative Gaussian noise, by examining qualitative changes in mean phase portraits. Starting from the Fokker-Planck equation for the probability density function of…
Considerable evidence suggests that anticipating sudden shifts from one state to another in bistable dynamical systems is a challenging task, examples include ecosystems, financial markets, complex diseases, etc. In this paper, we…
Here we investigate single-cell stochastic gene expression kinetics in a minimal coupled gene circuit with positive-plus-negative feedback. A triphasic stochastic bifurcation upon the increasing ratio of the positive and negative feedback…
Many cellular functions are based on the rhythmic organization of biological processes into self-repeating cascades of events. Some of these periodic processes, such as the cell cycles of several species, exhibit conspicuous irregularities…
Two synthetic gene circuits -- the genetic toggle switch and the repressilator -- are analyzed quantitatively and discussed in the context of an educational module on gene circuits and feedback that constitutes the final topic of a…
Gene regulatory circuits show significant stochastic fluctuations in their circuit signals due to the low copy number of transcription factors. When a gene circuit component is connected to an existing circuit, the dynamic properties of the…
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…
The intrinsic stochasticity of gene expression can lead to large variability in protein levels for genetically identical cells. Such variability in protein levels can arise from infrequent synthesis of mRNAs which in turn give rise to…
The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several…