Related papers: Reconstructing bifurcation behavior of a nonlinear…

We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the…

Bifurcation analysis has many applications in different scientific fields, such as electronics, biology, ecology, and economics. In population biology, deterministic methods of bifurcation are commonly used. In contrast, stochastic…

In this paper we propose a new method to detect and classify coexisting solutions in nonlinear systems. We focus on mechanical and structural systems where we usually avoid multistability for safety and reliability. We want to be sure that…

Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…

Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In…

Robust oscillations play crucial roles in a wide variety of biological processes and are often generated by deterministic mechanisms. However, stochastic fluctuations often generate complex perturbations of these deterministic oscillations,…

System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear…

We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact…

Suppose a two-dimensional dynamical system has a stable attractor that is surrounded by an unstable limit cycle. If the system is additively perturbed by white noise, the rate of escape through the limit cycle will fall off exponentially as…

In this paper, we derive a novel procedure for set-membership estimation of dynamical systems affected by stochastic noise with unbounded support. Employing a bound on the sample covariance matrix, we are able to provide a finite- sample…

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…

Previous studies have shown that noise can induce coherence resonance in some nonlinear dynamical systems close to a bifurcation of a periodic motion, such as in excitable systems. We demonstrate that coherence resonance can be observed in…

Nonlinear dynamical systems possessing reflection symmetry have an invariant subspace in the phase space. The dynamics within the invariant subspace can be random or chaotic. As a system parameter changes, the motion transverse to the…

In a noisy environment, oscillations loose their coherence which can be characterized by a quality factor. We determine this quality factor for oscillations arising from a driven Fokker-Planck dynamics along a periodic one-dimensional…

We consider a prototypical nonlinear system which can be stabilized by multiplicative noise: an underdamped non-linear pendulum with a stochastically vibrating pivot. A numerical solution of the pertinent Fokker-Planck equation shows that…

The problem of determining dynamical models and trajectories that describe observed time-series data allowing for the understanding, prediction and possibly control of complex systems in nature is of a great interest in a wide variety of…

The relaxation to equilibrium in many systems which show strange kinetics is described by fractional Fokker-Planck equations (FFPEs). These can be considered as phenomenological equations of linear nonequilibrium theory. We show that the…

It is well-known that the fundamental diagram in a realistic traffic system is featured by capacity drop. From a mesoscopic approach, we demonstrate that such a phenomenon is linked to the unique properties of stochastic noise, which, when…

We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though a weak noise is considered, we are interested in probabilities of large fluctuations (generally…

We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it…