PUB - Publikationen an der Universität Bielefeld

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)