Related papers: Knowing when to stop: how noise frees us from dete…
All physical systems are affected by some noise that limits the resolution that can be attained in partitioning their state space. For chaotic, locally hyperbolic flows, this resolution depends on the interplay of the local…
The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions…
Weak noise smooths out fractals in a chaotic state space and introduces a maximum attainable resolution to its structure. The balance of noise and deterministic stretching/contraction in each neighborhood introduces local invariants of the…
We consider a 2-dimensional stochastic differential equation in polar coordinates depending on several parameters. We show that if these parameters belong to a specific regime then the deterministic system explodes in finite time, but the…
The optimized expansion is used to formulate a systematic approximation scheme to the probability distribution of a stochastic system. The first order approximation for the one-dimensional system driven by noise in an anharmonic potential…
We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or…
Stationary solutions to a Fokker-Planck equation corresponding to a noisy logistic equation with correlated Gaussian white noises are constructed. Stationary distributions exist even if the corresponding deterministic system displays an…
In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…
The existence and characterisation of noise-driven bifurcations from the spatially homogeneous stationary states of a nonlinear, non-local Fokker--Planck type partial differential equation describing stochastic neural fields is established.…
The aim of this contribution is to study the particle dynamics in a storage ring under the influence of noise. Some simplified stochastic beam dynamics problems are treated by solving the corresponding Fokker-Planck equations numerically.
The paper considers a stabilizing stochastic control which can be applied to a variety of unstable and even chaotic maps. Compared to previous methods introducing control by noise, we relax assumptions on the class of maps, as well as…
Quantum tunneling in the presence of chaos is analyzed, focusing especially on the interplay between quantum tunneling and dynamical localization. We observed flooding of potentially existing tunneling amplitude by adding noise to the…
We develop a prototypical stochastic model for local search around a given home. The stochastic dynamic model is motivated by experimental findings of the motion of a fruit fly around a given spot of food but shall generally describe local…
Dynamics of a system that performs a large fluctuation to a given state is essentially deterministic: the distribution of fluctuational paths peaks sharply at a certain optimal path along which the system is most likely to move. For the…
We characterize a stochastic dynamical system with tempered stable noise, by examining its probability density evolution. This probability density function satisfies a nonlocal Fokker-Planck equation. First, we prove a superposition…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…
We use an effective Hamiltonian to characterize particle dynamics and find escape rates in a periodically kicked Hamiltonian. We study a model of particles in storage rings that is described by a chaotic symplectic map. Ignoring the…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An…
We consider a dynamical system with finitely many equilibria and perturbed by small noise, in addition to being controlled by an `expensive' control. The controlled process is optimal for an ergodic criterion with a running cost that…