Supplementary Material for "Polyrhythmic Organization of Coupled Nonlinear Oscillators"

Baier G, Hermann T, Müller M (2005)
Bielefeld University.

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Baier, Gerold; Hermann, ThomasUniBi ; Müller, Markus
Abstract / Bemerkung
We study the rhythmic organization of coupled nonlinear oscillators. If oscillators with non-identical internal frequency are coupled, they generate a great variety of periodic and chaotic rhythmic patterns. Sonification of these patterns suggests their characterization in terms of polyrhythms: each oscillatory unit subdivides "measures" of equal or varying length differently. For the case of two coupled oscillators, the organization of these polyrhythms is exemplified as a function of the internal frequency ratio and the coupling strength. Some sonification strategies are presented which aid to detect complex rhythmic relationships between oscillators. The results may be of importance for the analysis of complex multivariate time series like human EEG. * A 4:3 Polyrhythm with parameters as in Fig. 2 * S1 (mp3, 306k) epsilon=0.75, D=0.005
* A chaotic polyrhythm with parameters as in Fig. 3 in two different speeds * S2a (mp3,494k) epsilon=0.74, D=0.005
* S2b (mp3, 1.2M) epsilon=0.74, D=0.005, T=50sec
* An intermittent polyrhythm with parameters I=0.0605, epsilon=0.6445, D=0.005 * S3 (mp3, 329k) T = 20sec
* A polyrhythm in a 3 oscillator system with internal frequencies set to 5:4:3 and D=0.01 * S4 (mp3, 1.4M)
* A chaotic polyrhythm in a three oscillator system with internal frequencies set to 1.0:0.9:0.55 and D=0.0032 (other parameters as in eq. 1). * S5a (mp3, 5sec, 95k)
* S5b (mp3, 15sec, 250k)
* S5c (mp3, 45sec, 720k)
* Sequence of rhythms as parameter epsilon is continuously varied from 0.5 to 0.99 * S6 (mp3, 494k)
* Sequence of rhythms as in S5 but with total duration 60 sec * S7 (mp3, 1.4M)
Erscheinungsjahr
2005
Page URI
https://pub.uni-bielefeld.de/record/2700951

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Baier G, Hermann T, Müller M. Supplementary Material for "Polyrhythmic Organization of Coupled Nonlinear Oscillators". Bielefeld University; 2005.
Baier, G., Hermann, T., & Müller, M. (2005). Supplementary Material for "Polyrhythmic Organization of Coupled Nonlinear Oscillators". Bielefeld University. doi:10.4119/unibi/2700951
Baier, G., Hermann, T., and Müller, M. (2005). Supplementary Material for "Polyrhythmic Organization of Coupled Nonlinear Oscillators". Bielefeld University.
Baier, G., Hermann, T., & Müller, M., 2005. Supplementary Material for "Polyrhythmic Organization of Coupled Nonlinear Oscillators", Bielefeld University.
G. Baier, T. Hermann, and M. Müller, Supplementary Material for "Polyrhythmic Organization of Coupled Nonlinear Oscillators", Bielefeld University, 2005.
Baier, G., Hermann, T., Müller, M.: Supplementary Material for "Polyrhythmic Organization of Coupled Nonlinear Oscillators". Bielefeld University (2005).
Baier, Gerold, Hermann, Thomas, and Müller, Markus. Supplementary Material for "Polyrhythmic Organization of Coupled Nonlinear Oscillators". Bielefeld University, 2005.
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Volltext(e)
Beschreibung
A 4:3 Polyrhythm with parameters as in Fig. 2.
epsilon=0.75, D=0.005 (mp3, 306k).
Access Level
OA Open Access
Zuletzt Hochgeladen
2019-09-25T06:34:41Z
MD5 Prüfsumme
56c7a747107fbd2c9bf1339ff308aa4a
Beschreibung
A chaotic polyrhythm with parameters as in Fig. 3 in two different speeds.
epsilon=0.74, D=0.005 (mp3,494k).
Access Level
OA Open Access
Zuletzt Hochgeladen
2019-09-25T06:34:41Z
MD5 Prüfsumme
35b5b83ef321633c705a64f99a4c359e
Beschreibung
A chaotic polyrhythm with parameters as in Fig. 3 in two different speeds.
epsilon=0.74, D=0.005, T=50sec (mp3, 1.2M).
Access Level
OA Open Access
Zuletzt Hochgeladen
2019-09-25T06:34:41Z
MD5 Prüfsumme
902310fb511ea7c3a447d118a21d5cff
Beschreibung
An intermittent polyrhythm with parameters I=0.0605, epsilon=0.6445, D=0.005, T = 20sec (mp3, 329k).
Access Level
OA Open Access
Zuletzt Hochgeladen
2019-09-25T06:34:41Z
MD5 Prüfsumme
2cc34c54278c63188c2c85efe2da8128
Beschreibung
A polyrhythm in a 3 oscillator system with internal frequencies set to 5:4:3 and D=0.01 (mp3, 1.4M).
Access Level
OA Open Access
Zuletzt Hochgeladen
2019-09-25T06:34:41Z
MD5 Prüfsumme
23523a28709859ca9ba372d8c193f3e2
Beschreibung
Sequence of rhythms as parameter epsilon is continuously varied from 0.5 to 0.99 (mp3, 494k).
Access Level
OA Open Access
Zuletzt Hochgeladen
2019-09-25T06:34:41Z
MD5 Prüfsumme
1c11a485352a9251e42ff968e9cf017d
Beschreibung
Sequence of rhythms as in S5 but with total duration 60 sec (mp3, 1.4M).
Access Level
OA Open Access
Zuletzt Hochgeladen
2019-09-25T06:34:41Z
MD5 Prüfsumme
6faf7e9e857b2a692eb18661351141cf
Beschreibung
A chaotic polyrhythm in a three oscillator system with internal frequencies set to 1.0:0.9:0.55 and D=0.0032 (other parameters as in eq. 1) (mp3, 5sec, 95k).
Access Level
OA Open Access
Zuletzt Hochgeladen
2019-09-25T06:34:41Z
MD5 Prüfsumme
2103509d8170d2824b93a0b1412fd319
Beschreibung
A chaotic polyrhythm in a three oscillator system with internal frequencies set to 1.0:0.9:0.55 and D=0.0032 (other parameters as in eq. 1) (mp3, 15sec, 250k).
Access Level
OA Open Access
Zuletzt Hochgeladen
2019-09-25T06:34:41Z
MD5 Prüfsumme
e8844b84e162be7b17cda9db2956c773
Beschreibung
A chaotic polyrhythm in a three oscillator system with internal frequencies set to 1.0:0.9:0.55 and D=0.0032 (other parameters as in eq. 1) (mp3, 45sec, 720k).
Access Level
OA Open Access
Zuletzt Hochgeladen
2019-09-25T06:34:41Z
MD5 Prüfsumme
3fcf6e9a7ba6dd749917a8e49b1a05b9

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Polyrhythmic Organization of Coupled Nonlinear Oscillators
Baier G, Hermann T, Müller M (2005)
In: IV' 05: Proceedings of the Ninth International Conference on Information Visualisation (IV'05). Los Alamitos, CA, USA: IEEE Computer Society: 5-10.

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