### Abstract

A simplified one-dimensional model system is introduced and studied here that exhibits intrinsic chaos with many degrees of freedom as well as increased predictability and slower decay of correlations for the large-scale features of the system. These are important features in common with vastly more complex problems involving climate modeling or molecular biological systems. This model is a suitable approximation of the Burgers-Hopf equation involving Galerkin projection on Fourier modes. The model has a detailed mathematical structure that leads to a well-defined equilibrium statistical theory as well as a simple scaling theory for correlations. The numerical evidence presented here strongly supports the behavior predicted from these statistical theories. Unlike the celebrated dissipative and dispersive approximations of the Burgers-Hopf equation, which exhibit exactly solvable and/or completely integrable behavior, these model approximations have strong intrinsic chaos with ergodic behavior.

Original language | English (US) |
---|---|

Pages (from-to) | 12413-12417 |

Number of pages | 5 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Volume | 97 |

Issue number | 23 |

DOIs | |

State | Published - 2000 |

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### ASJC Scopus subject areas

- General
- Genetics

### Cite this

*Proceedings of the National Academy of Sciences of the United States of America*,

*97*(23), 12413-12417. https://doi.org/10.1073/pnas.230433997

**Remarkable statistical behavior for truncated Burgers-Hopf dynamics.** / Maida, A. J.; Timofeyev, I.

Research output: Contribution to journal › Article

*Proceedings of the National Academy of Sciences of the United States of America*, vol. 97, no. 23, pp. 12413-12417. https://doi.org/10.1073/pnas.230433997

}

TY - JOUR

T1 - Remarkable statistical behavior for truncated Burgers-Hopf dynamics

AU - Maida, A. J.

AU - Timofeyev, I.

PY - 2000

Y1 - 2000

N2 - A simplified one-dimensional model system is introduced and studied here that exhibits intrinsic chaos with many degrees of freedom as well as increased predictability and slower decay of correlations for the large-scale features of the system. These are important features in common with vastly more complex problems involving climate modeling or molecular biological systems. This model is a suitable approximation of the Burgers-Hopf equation involving Galerkin projection on Fourier modes. The model has a detailed mathematical structure that leads to a well-defined equilibrium statistical theory as well as a simple scaling theory for correlations. The numerical evidence presented here strongly supports the behavior predicted from these statistical theories. Unlike the celebrated dissipative and dispersive approximations of the Burgers-Hopf equation, which exhibit exactly solvable and/or completely integrable behavior, these model approximations have strong intrinsic chaos with ergodic behavior.

AB - A simplified one-dimensional model system is introduced and studied here that exhibits intrinsic chaos with many degrees of freedom as well as increased predictability and slower decay of correlations for the large-scale features of the system. These are important features in common with vastly more complex problems involving climate modeling or molecular biological systems. This model is a suitable approximation of the Burgers-Hopf equation involving Galerkin projection on Fourier modes. The model has a detailed mathematical structure that leads to a well-defined equilibrium statistical theory as well as a simple scaling theory for correlations. The numerical evidence presented here strongly supports the behavior predicted from these statistical theories. Unlike the celebrated dissipative and dispersive approximations of the Burgers-Hopf equation, which exhibit exactly solvable and/or completely integrable behavior, these model approximations have strong intrinsic chaos with ergodic behavior.

UR - http://www.scopus.com/inward/record.url?scp=0033751055&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033751055&partnerID=8YFLogxK

U2 - 10.1073/pnas.230433997

DO - 10.1073/pnas.230433997

M3 - Article

C2 - 11050184

AN - SCOPUS:0033751055

VL - 97

SP - 12413

EP - 12417

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 23

ER -