Related papers: Mapping densities in a noisy state space

Deterministic chaotic dynamics presumes that the state space can be partitioned arbitrarily finely. In a physical system, the inevitable presence of some noise sets a finite limit to the finest possible resolution that can be attained. Much…

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…

A linear Gaussian state-space smoothing algorithm is presented for estimation of derivatives from a sequence of noisy measurements. The algorithm uses numerically stable square-root formulas, can handle simultaneous independent measurements…

A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time…

We investigate a model where strong noise in a sub-population creates a metastable state in an otherwise unstable two-population system. The induced metastable state is vortex-like, and its persistence time grows exponentially with the…

The dynamics of well-mixed biological populations is usually studied by mean-field methods and weak-noise expansions. Similar methods have been applied also in spatially extended problems, relying on the fact that these populations are…

We study the quantum dynamics generated by a non-Hermitian Hamiltonian subject to stochastic perturbations in its anti-Hermitian part, describing fluctuating gains and losses. The dynamics averaged over the noise is described by an…

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…

This paper presents a systematic numerical study of the effects of noise on the invariant probability densities of dynamical systems with varying degrees of hyperbolicity. It is found that the rate of convergence of invariant densities in…

We study the effect of local unitary noise on the entanglement evolution of a two-qubit system subject to local monitoring and inter-qubit coupling. We construct a stochastic Hamiltonian by incorporating the noise into the…

We consider the usage of dynamical decoupling in quantum metrology, where the joint evolution of system plus environment is described by a Hamiltonian. We demonstrate that by ultra-fast unitary control operations acting locally only on…

Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…

We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…

We study the dynamics of an inertial particle coupled to forcing, dissipation, and noise in the small mass limit. We derive an expression for the limiting (homogenized) joint distribution of the position and (scaled) velocity degrees of…

Complete characterization of a noisy multipartite quantum state in terms of entanglement requires full knowledge of how the entanglement content in the state is affected by the spatial distribution of noise in the state. Specifically, we…

We use particle dynamics simulations to probe the correlations between noise and dynamics in a variety of disordered systems, including superconducting vortices, 2D electron liquid crystals, colloids, domain walls, and granular media. The…

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…

The influence of an external random field on the competition process in a nonlinear open spatially extended system is analyzed numerically. A three-component model is chosen as the competition model in which a "weak" species can move in…

Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated…

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…