### 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 |

State | Published - Jul 2013 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Memoirs of the American Mathematical Society*,

*224*(1054), 1-97.

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

Research output: Contribution to journal › Article

*Memoirs of the American Mathematical Society*, vol. 224, no. 1054, pp. 1-97.

}

TY - JOUR

T1 - Strange attractors for periodically forced parabolic equations

AU - Lu, Kening

AU - Wang, Qiu-Dong

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

UR - http://www.scopus.com/inward/record.url?scp=84878812752&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878812752&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84878812752

VL - 224

SP - 1

EP - 97

JO - Memoirs of the American Mathematical Society

JF - Memoirs of the American Mathematical Society

SN - 0065-9266

IS - 1054

ER -