### Abstract

The success of deterministic modeling of a physical system relies on whether the solution of the model would approximate the dynamics of the actual system. When the system is chaotic, situations can arise where periodic orbits embedded in the chaotic set have distinct number of unstable directions and, as a consequence, no model of the system produces reasonably long trajectories that are realized by nature. We argue and present physical examples indicating that, in such a case, though the model is deterministic and low dimensional, statistical quantities can still be reliably computed. [S1063-651X(99)10302-7].

Original language | English |
---|---|

Pages (from-to) | 2907-2910 |

Number of pages | 4 |

Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 59 |

Issue number | 3 |

Publication status | Published - Mar 1999 |

### Keywords

- dynamic-systems
- trajectories
- crises
- sets

### Cite this

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*59*(3), 2907-2910.

**Modeling of deterministic chaotic systems.** / Lai, Y C ; Grebogi, C ; Kurths, J ; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 59, no. 3, pp. 2907-2910.

}

TY - JOUR

T1 - Modeling of deterministic chaotic systems

AU - Lai, Y C

AU - Grebogi, C

AU - Kurths, J

AU - Lai, Ying-Cheng

PY - 1999/3

Y1 - 1999/3

N2 - The success of deterministic modeling of a physical system relies on whether the solution of the model would approximate the dynamics of the actual system. When the system is chaotic, situations can arise where periodic orbits embedded in the chaotic set have distinct number of unstable directions and, as a consequence, no model of the system produces reasonably long trajectories that are realized by nature. We argue and present physical examples indicating that, in such a case, though the model is deterministic and low dimensional, statistical quantities can still be reliably computed. [S1063-651X(99)10302-7].

AB - The success of deterministic modeling of a physical system relies on whether the solution of the model would approximate the dynamics of the actual system. When the system is chaotic, situations can arise where periodic orbits embedded in the chaotic set have distinct number of unstable directions and, as a consequence, no model of the system produces reasonably long trajectories that are realized by nature. We argue and present physical examples indicating that, in such a case, though the model is deterministic and low dimensional, statistical quantities can still be reliably computed. [S1063-651X(99)10302-7].

KW - dynamic-systems

KW - trajectories

KW - crises

KW - sets

M3 - Article

VL - 59

SP - 2907

EP - 2910

JO - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 3

ER -