Related papers: Numerical detection of stochastic to deterministic…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
Some physical processes, including the intensity fluctuations of a chaotic laser, the detection of single photons, and the Brownian motion of a microscopic particle in a fluid are unpredictable, at least on long timescales. This…
Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies. A computational analysis is conducted to…
In this study, we estimate parameters in stochastic oscillatory systems by developing a novel cost function. This function incorporates power spectral density, analytic signal, and position crossings, each weighted to capture distinct…
The effect of small-amplitude noise on excitable systems with large time-scale separation is analyzed. It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle…
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…
Using numerical simulations of a model disk system, we demonstrate that a machine learning generated order parameter can detect depinning transitions and different dynamic flow phases in systems driven far from equilibrium. We specifically…
The effects of intrinsic noise on stochastic delay systems is studied within an expansion in the inverse system size. We show that the stochastic nature of the underlying dynamics may induce oscillatory behaviour in parameter ranges where…
In a recent letter [Phys.Rev.Lett. {\bf 30}, 3269 (1995), chao-dyn/9510011], we reported that a macroscopic chaotic determinism emerges in a multistable system: the unidirectional motion of a dissipative particle subject to an apparently…
We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic busting. We…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
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…
We studied non-dynamical stochastic resonance for the number of trades in the stock market. The trade arrival rate presents a deterministic pattern that can be modeled by a cosine function perturbed by noise. Due to the nonlinear…
Nanolasers operating at low power levels are strongly affected by intrinsic quantum noise, influencing both intensity fluctuations and laser coherence. Starting from semiclassical rate equations and making a simple hypothesis for the phase…
We consider a stochastic process with long-range dependence perturbed by multiplicative noise. The marginal distributions of both the original process and the noise have regularly-varying tails, with tail indices $\alpha,\alpha'>0$,…
We use a recently developed order parameter expansion method to study the transition to synchronous firing occuring in a system of coupled active rotators under the exclusive presence of quenched noise. The method predicts correctly the…
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
"\textit{The noise is the signal}"[R. Landauer, Nature \textbf{392}, 658 (1998)] emphasizes the rich information content encoded in fluctuations. This paper assesses the dynamical role of fluctuations of a quantum system driven far from…
We perturb with an additive Gaussian white noise the Hamiltonian system associated to a cubic anharmonic oscillator. The stochastic system is assumed to start from initial conditions that guarantee the existence of a periodic solution for…
Intrinsic or demographic noise has been shown to play an important role in the dynamics of a variety of systems including predator-prey populations, intracellular biochemical reactions, and oscillatory chemical reaction systems, and is…