Strange attractors for periodically forced parabolic equations

Kening Lu, Qiu-Dong Wang, Lai Sang Young

Research output: Contribution to journalArticle

12 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)1-97
Number of pages97
JournalMemoirs of the American Mathematical Society
Volume224
Issue number1054
StatePublished - Jul 2013
Externally publishedYes

Fingerprint

Strange attractor
Hopf bifurcation
Shearing
Partial differential equations
Parabolic Equation
SRB Measure
Concretes
Periodic Forcing
Infinite-dimensional Systems
Chaotic Behavior
Hopf Bifurcation
Partial differential equation

Keywords

  • Hopf bifurcations
  • Parabolic PDEs
  • Periodic forcing
  • SRB measures
  • Strange attractors

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Strange attractors for periodically forced parabolic equations. / Lu, Kening; Wang, Qiu-Dong; Young, Lai Sang.

In: Memoirs of the American Mathematical Society, Vol. 224, No. 1054, 07.2013, p. 1-97.

Research output: Contribution to journalArticle

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