Bifurcations of set-valued dynamical systems

We study families of set-valued dynamical systems and show how minimal invariant sets depend on parameters. We give a variant on the definition of attractor repeller pairs and obtain a different version of the Conley decomposition theorem. Under mild conditions on these systems we show that minimal...

Full description

Bibliographic Details
Main Author:	Athorne, Alexander
Other Authors:	Rasmussen, Martin ; Lamb, Jeroen
Published:	Imperial College London 2017
Subjects:	510
Online Access:	https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.754715

id	ndltd-bl.uk-oai-ethos.bl.uk-754715
record_format	oai_dc
spelling	ndltd-bl.uk-oai-ethos.bl.uk-7547152019-03-05T15:34:00ZBifurcations of set-valued dynamical systemsAthorne, AlexanderRasmussen, Martin ; Lamb, Jeroen2017We study families of set-valued dynamical systems and show how minimal invariant sets depend on parameters. We give a variant on the definition of attractor repeller pairs and obtain a different version of the Conley decomposition theorem. Under mild conditions on these systems we show that minimal invariant sets are related to a variation on the definition of chain components we call orbitally connected sets. We show for such systems that bifurcations can occur as a result of two orbitally connected sets colliding.510Imperial College Londonhttps://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.754715http://hdl.handle.net/10044/1/62323Electronic Thesis or Dissertation
collection	NDLTD
sources	NDLTD
topic	510
spellingShingle	510 Athorne, Alexander Bifurcations of set-valued dynamical systems
description	We study families of set-valued dynamical systems and show how minimal invariant sets depend on parameters. We give a variant on the definition of attractor repeller pairs and obtain a different version of the Conley decomposition theorem. Under mild conditions on these systems we show that minimal invariant sets are related to a variation on the definition of chain components we call orbitally connected sets. We show for such systems that bifurcations can occur as a result of two orbitally connected sets colliding.
author2	Rasmussen, Martin ; Lamb, Jeroen
author_facet	Rasmussen, Martin ; Lamb, Jeroen Athorne, Alexander
author	Athorne, Alexander
author_sort	Athorne, Alexander
title	Bifurcations of set-valued dynamical systems
title_short	Bifurcations of set-valued dynamical systems
title_full	Bifurcations of set-valued dynamical systems
title_fullStr	Bifurcations of set-valued dynamical systems
title_full_unstemmed	Bifurcations of set-valued dynamical systems
title_sort	bifurcations of set-valued dynamical systems
publisher	Imperial College London
publishDate	2017
url	https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.754715
work_keys_str_mv	AT athornealexander bifurcationsofsetvalueddynamicalsystems
_version_	1718994396042493952

Bifurcations of set-valued dynamical systems

Similar Items