Strange attractors for periodically forced parabolic equations

Kening Lu; Qiudong Wang; Lai Sang Young

doi:10.1090/s0065-9266-2012-00669-1

Strange attractors for periodically forced parabolic equations

Kening Lu, Qiudong Wang, Lai Sang Young

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We prove that in systems undergoing Hopf bifurcations, the effects of periodic forcing can be amplified by the shearing in the system to create sustained chaotic behavior. Specifically, strange attractors with SRB measures are shown to exist. The analysis is carried out for infinite dimensional systems, and the results are applicable to partial differential equations. Application of the general results to a concrete equation, namely the Brusselator, is given.

Original language	English (US)
Pages (from-to)	1-97
Number of pages	97
Journal	Memoirs of the American Mathematical Society
Volume	224
Issue number	1054
DOIs	https://doi.org/10.1090/s0065-9266-2012-00669-1
State	Published - Jul 2013

Keywords

Hopf bifurcations
Parabolic PDEs
Periodic forcing
SRB measures
Strange attractors

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/s0065-9266-2012-00669-1

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abstract = "We prove that in systems undergoing Hopf bifurcations, the effects of periodic forcing can be amplified by the shearing in the system to create sustained chaotic behavior. Specifically, strange attractors with SRB measures are shown to exist. The analysis is carried out for infinite dimensional systems, and the results are applicable to partial differential equations. Application of the general results to a concrete equation, namely the Brusselator, is given.",

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T1 - Strange attractors for periodically forced parabolic equations

AU - Lu, Kening

AU - Wang, Qiudong

AU - Young, Lai Sang

PY - 2013/7

Y1 - 2013/7

N2 - We prove that in systems undergoing Hopf bifurcations, the effects of periodic forcing can be amplified by the shearing in the system to create sustained chaotic behavior. Specifically, strange attractors with SRB measures are shown to exist. The analysis is carried out for infinite dimensional systems, and the results are applicable to partial differential equations. Application of the general results to a concrete equation, namely the Brusselator, is given.

AB - We prove that in systems undergoing Hopf bifurcations, the effects of periodic forcing can be amplified by the shearing in the system to create sustained chaotic behavior. Specifically, strange attractors with SRB measures are shown to exist. The analysis is carried out for infinite dimensional systems, and the results are applicable to partial differential equations. Application of the general results to a concrete equation, namely the Brusselator, is given.

KW - Hopf bifurcations

KW - Parabolic PDEs

KW - Periodic forcing

KW - SRB measures

KW - Strange attractors

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JO - Memoirs of the American Mathematical Society

JF - Memoirs of the American Mathematical Society

IS - 1054

ER -

Strange attractors for periodically forced parabolic equations

Abstract

Keywords

ASJC Scopus subject areas

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