1986
DOI: 10.1016/0375-9601(86)90210-0
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Calculating the dimension of attractors from small data sets

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Cited by 133 publications
(31 citation statements)
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“…On the contrary, nonlinear tools focus more on how the motion pattern changes over time (Dingwell & Cusumano, 2000;Hausdorff, Edelberg, & Michell, 1997). Therefore, when observing the stability of a specific variable in running, nonlinear tools can study the changes of stride-to-stride cycles during a longer period, making it advantageous to observing the original conserved data and to analyzing the uniqueness of a system (Abraham et al, 1986).…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…On the contrary, nonlinear tools focus more on how the motion pattern changes over time (Dingwell & Cusumano, 2000;Hausdorff, Edelberg, & Michell, 1997). Therefore, when observing the stability of a specific variable in running, nonlinear tools can study the changes of stride-to-stride cycles during a longer period, making it advantageous to observing the original conserved data and to analyzing the uniqueness of a system (Abraham et al, 1986).…”
Section: Discussionmentioning
confidence: 99%
“…Furthermore, in a study that used the coupling angle of the body segment and joints to predict the injury mechanism caused by running, only one or two strides were chosen for the analysis after assuming the running stride as a perfect periodic movement. As a result, the unique characteristics of the neurological muscle system acting on the stride during running were disregarded in the time-series state (Abraham et al, 1986).…”
mentioning
confidence: 99%
“…Such lengthy data sets do not exist in oceanography, so methods that work with short data sets (see for example, Ellner (1988), Havstad and Ehlers (1989) or Abraham et al, 1986) must be used. Also the presence of noise (either due to measurement errors or to small scale oceanic process) complicates the calculations.…”
Section: Practical Problems In Estimating Chaotic Parameters From Actmentioning
confidence: 99%
“…According to a large body of literature,, large datasets are required to assess chaotic behaviour, but this is often not achievable due to cost, technical or temporal limitations (Abraham et al, 1986;Kantz, 1994;Rosenstein et al, 1993). Data scarcity can limit the power of the method to calculate λ ( Abraham et al, 1986;Kantz, 1994). However, a method has been introduced by Rosenstein et al (1993) to overcome this limitation, allowing sufficiently accurate and precise calculations of λ in small datasets (Becks et al, 2005;Graham et al, 2007;Kantz, 1994;Navarro-Urrios et al, 2017).…”
Section: Introductionmentioning
confidence: 99%
“…The most useful tool for examining the sensitivity to initial conditions and detecting the presence of chaotic behaviour has been the widely documented largest Lyapunov exponent (λ) method (Becks et al, 2005;Chen et al, 2016;Gaspard et al, 1998;Gottwald, 2009;Kodba et al, 2005;Navarro-Urrios et al, 2017;Panas, 2001;Panas and Ninni, 2000;Perc, 2006;Reynolds et al, 2016;Rosenstein et al, 1993;Savi, 2005;Showalter and Hamilton, 2015;Wernecke et al, 2017;Zhong et al, 2017). According to a large body of literature,, large datasets are required to assess chaotic behaviour, but this is often not achievable due to cost, technical or temporal limitations (Abraham et al, 1986;Kantz, 1994;Rosenstein et al, 1993). Data scarcity can limit the power of the method to calculate λ ( Abraham et al, 1986;Kantz, 1994).…”
Section: Introductionmentioning
confidence: 99%