相关论文: Predictive dynamical and stochastic systems

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…

The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…

The study of density-dependent stochastic population processes is important from a historical perspective as well as from the perspective of a number of existing and emerging applications today. In more recent applications of these…

A system's internal dynamics and its interaction with the environment can be determined by tracking how external perturbations affect its transition rates between states. Quantitative measurements of these rates are crucial for optimizing…

Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…

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…

Analysis is presented of a system whose dynamics are dramatically simplified by tiny amounts of additive noise. The dynamics divide naturally into two phases. In the slower phase, trajectories are close to an invariant manifold; this allows…

In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…

We have analyzed the interplay between noise and periodic spatial modulations in bistable systems outside equilibrium and found that noise is able to increase the spatial order of the system, giving rise to periodic patterns which otherwise…

We propose a modeling framework for stochastic systems, termed Gaussian behaviors, that describes finite-length trajectories of a system as a Gaussian process. The proposed model naturally quantifies the uncertainty in the trajectories, yet…

A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…

The dynamical evolution of many economic, sociological, biological and physical systems tends to be dominated by a relatively small number of unexpected, large changes (`extreme events'). We study the large, internal changes produced in a…

We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…

The effects of intrinsic noise on stochastic delay systems is studied within an expansion in the inverse system size. We show that the stochastic nature of the underlying dynamics may induce oscillatory behaviour in parameter ranges where…

Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the…

Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…

We study an extended system that without noise shows a spatially homogeneous state, but when submitted to an adequate multiplicative noise, some "noise-induced patterns" arise. The stochastic resonance between these structures is…

We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…

One of the central aims of neuroscience is to reliably predict the behavioral response of an organism using its neural activity. If possible, this implies we can causally manipulate the neural response and design brain-computer-interface…

This paper deals with the analysis of stochastic systems which can be described by a Langevin equation. By the method presented in this paper drift and diffusion terms of the corresponding Fokker-Planck equation can be extracted from the…