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Rate-Dependent Bifurcations and Isol...

ProQuest Information and Learning Co.

Rate-Dependent Bifurcations and Isolating Blocks in Nonautonomous Systems.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Rate-Dependent Bifurcations and Isolating Blocks in Nonautonomous Systems./
Author:	Hahn, Jonathan.
Description:	1 online resource (83 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-03(E), Section: B.
Contained By:	Dissertation Abstracts International79-03B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355521689

Rate-Dependent Bifurcations and Isolating Blocks in Nonautonomous Systems.
Hahn, Jonathan.

Rate-Dependent Bifurcations and Isolating Blocks in Nonautonomous Systems. - 1 online resource (83 pages)

Source: Dissertation Abstracts International, Volume: 79-03(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

We examine rate-dependent tipping and the behavior of solutions to nonautonomous systems from a topological perspective. We analyze an example of a rate-dependent bifurcation in which steady solutions begin to spiral, yet remain in a bounded region around a moving equilibrium. This example motivates us to develop a theory of isolating blocks for invariant sets in nonautonomous systems. Our examination of these isolating blocks reveals that solutions in rate-dependent systems are structurally stable; the rate-dependent forcing may have some amount of noise while the underlying behavior of solutions to the system remains the same. We also find isolating blocks useful for placing bounds on critical values for rate-dependent tipping in nonautonomous systems. Finally, we introduce rate-dependent tipping for discrete maps.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355521689Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Rate-Dependent Bifurcations and Isolating Blocks in Nonautonomous Systems.
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100 1 $a Hahn, Jonathan. $3 1180940
245 1 0 $a Rate-Dependent Bifurcations and Isolating Blocks in Nonautonomous Systems.
264 0 $c 2017
300 $a 1 online resource (83 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
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500 $a Source: Dissertation Abstracts International, Volume: 79-03(E), Section: B.
500 $a Adviser: Richard McGehee.
502 $a Thesis (Ph.D.) $c University of Minnesota $d 2017.
504 $a Includes bibliographical references
520 $a We examine rate-dependent tipping and the behavior of solutions to nonautonomous systems from a topological perspective. We analyze an example of a rate-dependent bifurcation in which steady solutions begin to spiral, yet remain in a bounded region around a moving equilibrium. This example motivates us to develop a theory of isolating blocks for invariant sets in nonautonomous systems. Our examination of these isolating blocks reveals that solutions in rate-dependent systems are structurally stable; the rate-dependent forcing may have some amount of noise while the underlying behavior of solutions to the system remains the same. We also find isolating blocks useful for placing bounds on critical values for rate-dependent tipping in nonautonomous systems. Finally, we introduce rate-dependent tipping for discrete maps.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Minnesota. $b Mathematics. $3 1180493
773 0 $t Dissertation Abstracts International $g 79-03B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10636591 $z click for full text (PQDT)

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