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## Chaos in Nonlinear Dynamical Systems – Helicopter Flight-data Analysis

### Citations

591 |
Chaos in dynamical systems
- Ott
- 1993
(Show Context)
Citation Context ...are NMR laser data, human breath rate [3], among others. If a system shows some signs of chaotic behavior, then it may be controlled with some of the methods which are proposed in the literature [3], =-=[4]-=-, [5]. In most real-life systems, system behavior is characterized by time-series data available from measurement. The first step in the analysis of time-series data was introduced in Geometry from a ... |

404 |
Independent coordinates for strange attractors from mutual information
- Fraser, Swinney
(Show Context)
Citation Context ... Fredericton, New Brunswick, CANADA E3B 5A3 E-mail: 1) jtaylor@unb.ca, 2) salamat@ee.unb.ca In delay-coordinate reconstruction, the selection of time delay and dimension are the most important issues =-=[7]-=-, [8]. By appropriate selection of time delay and embedding dimension, the time-series data can be reconstructed in the delay-coordinate state space. In this space, the chaotic behavior of the nonline... |

340 |
Chaos: An Introduction to Dynamical Systems
- Alligood, Sauer, et al.
- 1996
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Citation Context ...tems. Examples of classical systems include the logistic, tent and Hénon maps in the realm of discrete systems, and the Lorenz and Rössler differential equations for continuous-time dynamical systems =-=[2]-=-. Some real-life systems in which chaos has been identified are NMR laser data, human breath rate [3], among others. If a system shows some signs of chaotic behavior, then it may be controlled with so... |

293 |
Geometry from a time series
- Packard, Crutchfield, et al.
- 1980
(Show Context)
Citation Context ...st real-life systems, system behavior is characterized by time-series data available from measurement. The first step in the analysis of time-series data was introduced in Geometry from a time series =-=[6]-=-, in which state space reconstruction of time-series data was proposed for the first time. Department of Electrical and Computer Engineering, University of New Brunswick Fredericton, New Brunswick, CA... |

235 |
Determining embedding dimension for phase-space reconstruction using a geometrical construction
- Kennel, Brown, et al.
- 1992
(Show Context)
Citation Context ...ericton, New Brunswick, CANADA E3B 5A3 E-mail: 1) jtaylor@unb.ca, 2) salamat@ee.unb.ca In delay-coordinate reconstruction, the selection of time delay and dimension are the most important issues [7], =-=[8]-=-. By appropriate selection of time delay and embedding dimension, the time-series data can be reconstructed in the delay-coordinate state space. In this space, the chaotic behavior of the nonlinear dy... |

221 |
Detecting strange attractors in turbulence, in: Dynamical Systems and Turbulence
- Takens
- 1980
(Show Context)
Citation Context ...te state space. For this reason, time-series data should be converted into state space vectors. This procedure is known as state space reconstruction, which is based on a theorem attributed to Takens =-=[9]-=-. For many physical systems, a state space flow model, is not available; rather, observations of the system variables are taken, including measurements of one or several quantities which depends on th... |

166 | A practical method for calculating largest Lyapunov exponents from small data sets. Physica D: Nonlinear Phenomena
- Rosenstein, Collins, et al.
- 1993
(Show Context)
Citation Context ...em is discussed, and the next steps in this study are presented. I. INTRODUCTION An understanding of the identification and control of chaotic systems has improved tremendously in the last decade [1]-=-=[12]-=-. Chaotic behavior occurs in systems with nonlinear dynamics. The recognition of chaos in a complex dynamical system is very complicated. An important characteristic of a chaotic system is its sensiti... |

97 |
Abarbanel, Analysis of Observed Chaotic Data
- I
- 1996
(Show Context)
Citation Context ...system is discussed, and the next steps in this study are presented. I. INTRODUCTION An understanding of the identification and control of chaotic systems has improved tremendously in the last decade =-=[1]-=--[12]. Chaotic behavior occurs in systems with nonlinear dynamics. The recognition of chaos in a complex dynamical system is very complicated. An important characteristic of a chaotic system is its se... |

88 | State space reconstruction in the presence of noise
- Casdagli, Eubank, et al.
(Show Context)
Citation Context ...on of V has no effect on the embedding of a noise-free time series. However, in practical applications and for data contaminated with noise, a good choice of V has an important impact on the analysis =-=[4]-=-. If V is too small in comparison with the dynamic variation of the system, successive elements of the delay vectors are strongly correlated. If V is too large, successive elements are almost independ... |

87 |
Chaos and deterministic versus stochastic nonlinear modeling
- Casdagli
- 1992
(Show Context)
Citation Context ...pplications are discussed below. A. Time Delay Calculation: Autocorrelation Method In this approach, the autocorrelation function of the signal is used to identify the optimal value of sampling delay =-=[10]-=-. A commonly used rule of thumb [5] for the calculation of sampling lag is to set V equal to the sampling lag required for the autocorrelation function to become negative. The problem with this approa... |

86 | Measurement of the Lyapunov spectrum from a chaotic time series - Sano, Sawada - 1985 |

68 |
A robust method to estimate the maximal Lyapunov exponent of a time series. Phys Lett A
- Kantz
- 1994
(Show Context)
Citation Context ...This value can be measured as the average rate of the expansion/contraction, Dl, versus time steps, ∆k. In this calculation, only the points in the ɛ-neighborhood of each initial point are considered =-=[11]-=-. A. Calculation of the Maximal Lyapunov Exponent for Hénon Map and Lorenz System For verification of our analysis in the computation of maximal Lyapunov exponent, λ1, two classical chaotic examples a... |

34 |
Proper choice of the time delay for the analysis of chaotic time series
- Liebert, Schuster
- 1989
(Show Context)
Citation Context ...(one-to-one and invertible) equivalent to the original state space of the real-life system. In delay-coordinate reconstruction, the selection of time delay and dimension are the most important issues =-=[5, 9, 11, 12, 19]-=-. For the calculation of time lag, different approaches are proposed in the literature [5, 11]. Among them, the autocorrelation function and mutual information approach are the most general and common... |

30 |
Singular Value Decomposition and Embedding Dimension
- Rapp
- 1987
(Show Context)
Citation Context ...(one-to-one and invertible) equivalent to the original state space of the real-life system. In delay-coordinate reconstruction, the selection of time delay and dimension are the most important issues =-=[5, 9, 11, 12, 19]-=-. For the calculation of time lag, different approaches are proposed in the literature [5, 11]. Among them, the autocorrelation function and mutual information approach are the most general and common... |

29 |
Coping with Chaos: Analysis of Chaotic Data and the Exploitation of Chaotic Systems
- Ott, Sauer, et al.
- 1994
(Show Context)
Citation Context ...MR laser data, human breath rate [3], among others. If a system shows some signs of chaotic behavior, then it may be controlled with some of the methods which are proposed in the literature [3], [4], =-=[5]-=-. In most real-life systems, system behavior is characterized by time-series data available from measurement. The first step in the analysis of time-series data was introduced in Geometry from a time ... |

21 |
Communicating with chaos
- Hayes, Grebogi, et al.
- 1993
(Show Context)
Citation Context ...ry important implications for controlling nonlinear systems. If a systemsshows some signs of chaotic behaviour, then it may be controlled with some of the methods which are proposed in the literature =-=[6, 8, 10, 13, 14, 15]-=-. Chaos may exist in classical systems (represented by mathematical models) or reallife systems. Examples of classical systems include the logistic, tent and Hénon maps in the realm of discrete system... |

6 |
Christophersen N.: Chaotic time series
- Kugiumtzis, Lillekjendlie
- 1994
(Show Context)
Citation Context ...ry important implications for controlling nonlinear systems. If a systemsshows some signs of chaotic behaviour, then it may be controlled with some of the methods which are proposed in the literature =-=[6, 8, 10, 13, 14, 15]-=-. Chaos may exist in classical systems (represented by mathematical models) or reallife systems. Examples of classical systems include the logistic, tent and Hénon maps in the realm of discrete system... |

2 |
Controlling chaos, controlling chaotic dynamical systems
- Grebogi, Yorke
- 1996
(Show Context)
Citation Context ...ry important implications for controlling nonlinear systems. If a systemsshows some signs of chaotic behaviour, then it may be controlled with some of the methods which are proposed in the literature =-=[6, 8, 10, 13, 14, 15]-=-. Chaos may exist in classical systems (represented by mathematical models) or reallife systems. Examples of classical systems include the logistic, tent and Hénon maps in the realm of discrete system... |