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Vector fields that are discontinuous on codimension-one surfaces are known as Filippov systems and can have attracting periodic orbits involving segments that are contained on a discontinuity surface of the vector field. In this paper we…
Noise, through its interaction with the nonlinearity of the living systems, can give rise to counter-intuitive phenomena such as stochastic resonance, noise-delayed extinction, temporal oscillations, and spatial patterns. In this paper we…
This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input…
Cortical sensory neurons are known to be highly variable, in the sense that responses evoked by identical stimuli often change dramatically from trial to trial. The origin of this variability is uncertain, but it is usually interpreted as…
We ask whether most Boolean functions are determined by their low frequencies. We show a partial result: for almost every function $f: \{-1,1\}^p \to \{-1,1\}$ there exists a function $f': \{-1,1\}^p \to (-1,1)$ that has the same…
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…
In \cite{js2006}, Jonasson and Steif conjectured that no non-degenerate sequence of transitive Boolean functions $ (f_n)_{n \geq 1}$ with $ \lim_{n \to \infty} I(f_n)= \infty $ could be tame (with respect to some $ (p_n)_{n \geq 1} $). In a…
Phase transitions and effects of external noise on many body systems are one of the main topics in physics. In mean field coupled nonlinear dynamical stochastic systems driven by Brownian noise, various types of phase transitions including…
As a phenomenon in dynamical systems allowing autonomous switching between stable behaviors, chaotic itinerancy has gained interest in neurorobotics research. In this study, we draw a connection between this phenomenon and the predictive…
Additive noise in Partial Differential equations, in particular those of fluid mechanics, has relatively natural motivations. The aim of this work is showing that suitable multiscale arguments lead rigorously, from a model of fluid with…
Statistic dynamics of financial systems is investigated, basing on a model of randomly coupled equation system driven by stochastic Langevin force. It is found that in stable regime the noise power spectrum of the system is of 1/f^alpha…
This article studies the fluctuation behaviour of the stochastic point vortex model with common noise. Using the martingale method combined with a localization argument, we prove that the sequence of fluctuation processes converges in…
We investigate the dynamical behavior of pull-back trajectories for nonautonomous stochastic feedback systems with multiplicative noise. We proved that there exists a random periodic solution of this system and all pull-back trajectories…
A key fact in the theory of Boolean functions $f : \{0,1\}^n \to \{0,1\}$ is that they often undergo sharp thresholds. For example: if the function $f : \{0,1\}^n \to \{0,1\}$ is monotone and symmetric under a transitive action with…
We present a theoretical framework for characterizing incremental stability of nonlinear stochastic systems perturbed by compound Poisson shot noise and finite-measure L\'{e}vy noise. For each noise type, we compare trajectories of the…
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
Variable power transmission in mechanical systems is often achieved by devices, e.g., clutches and brakes, that use dry friction. In these systems, the variability in power transmission is brought about by engaging and disengaging the…
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…
In this article, we consider the dynamics in a neighborhood of a quasi-periodic torus which is invariant by a Hamiltonian flow, we discuss several notions of stability and we prove several results of instability when the frequency of the…
A lack of software reproducibility has become increasingly apparent in the last several years, calling into question the validity of scientific findings affected by published tools. Reproducibility issues may have numerous sources of error,…