Related papers: Geometric Methods for Stochastic Dynamical Systems
The observable behavior of a complex system reflects the mechanisms governing the internal interactions between the system's components and the effect of external perturbations. Here we show that by capturing the simultaneous activity of…
Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…
What features characterise complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue that slow,…
The occurrence of mesoscopic fluctuations in statistical systems implies, from the point of view of dynamical theory, the existence of local instabilities. However, the presence of such fluctuations can make a system, as a whole, more…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
This is the transcript of a talk given at the 1992 Complex Systems Summer School. The theory of large fluctuations of stochastically perturbed continuous-time dynamical systems is reviewed, and the large fluctuations of two stochastic…
Theoretical descriptions of the stepping-stone model, a cornerstone of spatial population genetics, have long overlooked diffusive noise arising from migration dynamics. We derive an exact fluctuating hydrodynamic description of this model…
Chemical reactions in cell are subject to intense stochastic fluctuations. An important question is how the fundamental physiological behavior of cell is kept stable against those noisy perturbations. In this paper a stochastic model of…
A genetic switch may be realised by a certain operator sector on the DNA strand from which either genetic code, to the left or to the right of this operator sector, can be transcribed and the corresponding information processed. This switch…
Many fluctuating systems consist of macroscopic structures in addition to noisy signals. Thus, for this class of fluctuating systems, the scaling behaviors are very complicated. Such phenomena are quite commonly observed in Nature, ranging…
In this work, we consider a multi-population system where the dynamics of each agent evolve according to a system of stochastic differential equations in a general functional setup, determined by the global state of the system. Each agent…
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…
We study the effect of intrinsic noise on the thermodynamic balance of complex chemical networks subtending cellular metabolism and gene regulation. A topological network property called deficiency, known to determine the possibility of…
Studies on the role of fluctuations in signal propagation and on gene regulation in monoclonal bacterial population have been extensively pursued based on the machinery of two-component system. The bacterial two-component system shows noise…
Single-cell studies often show significant phenotypic variability due to the stochastic nature of intra-cellular biochemical reactions. When the numbers of molecules, e.g., transcription factors and regulatory enzymes, are in low abundance,…
Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many…
The dynamics of a weakly dissipative Hamiltonian system submitted to stochastic perturbations has been investigated by means of asymptotic methods. The probability of noise-induced separatrix crossing, which drastically changes the fate of…
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…
Biological systems (among others) may respond to a large variety of distinct external stimuli, or signals. These perturbations will generally be presented to the system not singly, but in various combinations, so that a proper understanding…
We theoretically evaluate the impact of drift-free noise on the dynamics of $\mathcal{PT}$-symmetric non-Hermitian systems with an exceptional point, which have recently been proposed for sensors. Such systems are currently considered as…