Related papers: Stochastic calculus: application to dynamic bifurc…
This paper investigates the dynamic behavior of a simplified single reed instrument model subject to a stochastic forcing of white noise type when one of its bifurcation parameters (the dimensionless blowing pressure) increases linearly…
Statistical early warning signs can be used to identify an approaching bifurcation in stochastic dynamical systems and are now regularly employed in applications concerned with the identification of potential rapid, non-linear change or…
We investigate here various properties of the responses of excitable systems subject to periodic forcing and noise. While the properties of intrinsic oscillators, subject to added periodic signals, are well understood, much less is known…
A subthreshold signal is transmitted through a channel and may be detected when some noise -- with known structure and proportional to some level -- is added to the data. There is an optimal noise level, called stochastic resonance, that…
I study the dynamics of a Josephson junction serving as a threshold detector of fluctuations which is subjected to a general non-equilibrium electronic noise source whose characteristics is to be determined by the junction. This…
The problem of information extraction from discrete stochastic time series, produced with some finite sampling frequency, using flicker-noise spectroscopy, a general framework for information extraction based on the analysis of the…
We study noise-induced switching of a system close to bifurcation parameter values where the number of stable states changes. For non-Gaussian noise, the switching exponent, which gives the logarithm of the switching rate, displays a…
We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval $[0,T]$ via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class…
We consider a stochastic population model where the intrinsic or demographic noise causes cycling between states before the population eventually goes extinct. A master equation approach coupled with a WKB (Wentzel-Kramers-Brillouin)…
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…
It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependance on initial conditions (SDIC). Unfortunately, numerical noises (such as truncation error and round-off error)…
For a model nonlinear dynamical system, we show how one may obtain its bifurcation behavior by introducing noise into the dynamics and then studying the resulting Langevin dynamics in the weak-noise limit. A suitable quantity to capture the…
We propose a direct numerical method to calculate the statistics of the number of transitions in stochastic processes, without having to resort to Monte Carlo calculations. The method is based on a generating function method, and arbitrary…
Recently created diffusive memristors have garnered significant research interest owing to their distinctive capability to generate a diverse array of spike dynamics which are similar in nature to those found in biological cells. This gives…
We study a stochastic nonlocal PDE, arising in the context of modelling spatially distributed neural activity, which is capable of sustaining stationary and moving spatially-localized ``activity bumps''. This system is known to undergo a…
Incorporating probabilistic terms in mathematical models is crucial for capturing and quantifying uncertainties in real-world systems, especially when the solution is not unique or exhibits sudden qualitative changes as parameters vary.…
Control barrier functions are widely used to synthesize safety-critical controls. However, the presence of Gaussian-type noise in dynamical systems can generate unbounded signals and potentially result in severe consequences. Although…
Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants…
We consider certain one dimensional ordinary stochastic differential equations driven by additive Brownian motion of variance $\varepsilon ^2$. When $\varepsilon =0$ such equations have an unstable non-hyperbolic fixed point and the drift…
We study a noise-induced bifurcation in the vicinity of the threshold by using a perturbative expansion of the order parameter, called the Poincar\'e-Lindstedt expansion. Each term of this series becomes divergent in the long time limit if…