Related papers: Stochastic calculus: application to dynamic bifurc…

A numerical model based on the finite-difference time-domain method is developed to simulate fluctuations which accompany the dephasing of atomic polarization and the decay of excited state's population. This model is based on the…

Coarse timesteppers provide a bridge between microscopic / stochastic system descriptions and macroscopic tasks such as coarse stability/bifurcation computations. Exploiting this computational enabling technology, we present a framework for…

In this paper, we study the asymptotic behavior of the number of crossings by a one-dimensional diffusion of a threshold where the process exhibits stickiness. We distinguish three types of crossings and show that to each type corresponds a…

Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state…

We perform both analytical and numerical bifurcation analysis of a forest-grassland ecosystem model coupled with human interaction. The model consists of two nonlinear ordinary differential equations incorporating the human perception of…

We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that…

We propose a new test statistic based on a score process for determining the statistical significance of a putative signal that may be a small perturbation to a noisy experimental background. We derive the reference distribution for this…

Variability in neural responses is an ubiquitous phenomenon in neurons, usually modeled with stochastic differential equations. In particular, stochastic integrate-and-fire models are widely used to simplify theoretical studies. The…

Bifurcations of dynamical systems, described by a second order differential equations and by an impact condition are studied. It is shown that the variation of parameters when the number of impacts of a periodic solution increases, leads to…

Many complex real world phenomena exhibit abrupt, intermittent or jumping behaviors, which are more suitable to be described by stochastic differential equations under non-Gaussian L\'evy noise. Among these complex phenomena, the most…

We study a model for a dilute suspension of rod-like particles swimming at constant velocity in a Stokes flow. As the translational diffusivity of the particles decreases, a two-dimensional uniform concentration of randomly aligned…

Brain rhythms contribute to every aspect of brain function. Here, we study critical and resonance phenomena that precede the emergence of brain rhythms. Using an analytical approach and simulations of a cortical circuit model of neural…

Many real-world systems undergo abrupt changes in dynamics as they move across critical points, often with dramatic consequences. Much existing theory on identifying the time-series signatures of nearby critical points -- such as increased…

Using algorithms of Higuchi and of Grassberger and Procaccia, we study numerically how fractal dimensions cross over from finite-dimensional Brownian noise at short time scales to finite values of deterministic chaos at longer time scales…

Abrupt shifts in ecosystems, brains, markets, and climate are often diagnosed as signs of approaching a tipping point, i.e. a critical bifurcation where stability is lost. Here we reveal a broader and more deceptive mechanism:…

Many biological, chemical, and physical systems are underpinned by stochastic transitions between equilibrium states in a potential energy. Here, we consider such transitions in a minimal model with two possible competing pathways, both…

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…

We consider a dynamical system undergoing a saddle-node bifurcation with an explicitly time dependent parameter~$p(t)$. The combined dynamics can be considered as a dynamical systems where $p$ is a slowly evolving parameter. Here, we…

When a quantity reaches a value higher (or lower) than its value at any time before, it is said to have made a record. We numerically study the statistical properties of records in the time series of order parameters in different models…

Full counting statistics is a powerful tool to characterize the noise and correlations in transport through mesoscopic systems. In this work, we propose the theory of conditional spin counting statistics, i.e., the statistical fluctuations…