Bounds for bounded motion around a perturbed fixed point

Autor:	T. P. Valkering, R.M.J. van Damme
Jazyk:	angličtina
Rok vydání:	1988
Předmět:	Bounded perturbation Phase portrait Applied Mathematics General Mathematics Bounded function Numerical analysis Attractor Mathematical analysis Dissipative system General Physics and Astronomy Perturbation (astronomy) Fixed point Mathematics
Zdroj:	Zeitschrift für angewandte Mathematik und Physik, 39(6), 813-825. Birkhäuser
ISSN:	0044-2275
DOI:	10.1007/bf00945120
Popis:	We consider a dissipative map of the plane with a bounded perturbation term. This perturbation represents e.g. an extra time dependent term, a coupling to another system or noise. The unperturbed map has a spiral attracting fixed point. We derive an analytical/numerical method to determine the effect of the additional term on the phase portrait of the original map, as a function of the δ bound on the perturbation. This method yields a value δ c such that for δδ c the orbits about the attractor are certainly bounded. In that case we obtain a largest region in which all orbits remain bounded and a smallest region in which these bounded orbits are captured after some time (the analogue of 'basin' and 'attractor respectively').
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::10bddad65e9cacf17b5bf881ccf1610d https://doi.org/10.1007/bf00945120 Zobrazit plný text záznamu Full text from SpringerLink