Piecewise deterministic dynamics from the application of noise to singular equations of motion

Autor:	D D Dixon
Rok vydání:	1995
Předmět:	Nondeterministic algorithm Noise Singularity Phase space Mathematical analysis Piecewise Trajectory General Physics and Astronomy Equations of motion Statistical and Nonlinear Physics Lipschitz continuity Mathematical Physics Mathematics
Zdroj:	Journal of Physics A: Mathematical and General. 28:5539-5551
ISSN:	1361-6447 0305-4470
DOI:	10.1088/0305-4470/28/19/010
Popis:	We describe a form of piecewise deterministic dynamics, where solutions evolve deterministically throughout most of phase space, but, in the presence of noise, make nondeterministic jumps to other solutions when the trajectory passes near a singularity in the equations of motion. The type of singularity we consider in this paper is a single point where the Lipschitz conditions fail and many closed-loop trajectories share a common tangent point. It is shown that there is a finite uncertainty associated with the behaviour that is independent of the magnitude of the noise. The long-term behaviour, while similar in appearance to deterministic chaos, has rather different implications for prediction and control.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ca38e4639eab0438e1993bd73a242206 https://doi.org/10.1088/0305-4470/28/19/010 Zobrazit plný text záznamu