By Erik Mosekilde, Lis Mosekilde
Now and then, maybe once or twice each one century, a revolution happens that questions a few of our easy ideals and sweeps throughout in a different way good guarded disciplinary limitations. those are the classes while technological know-how is enjoyable, whilst new paradigms need to be formulated, and while younger scientists can do severe paintings with out first having to procure all of the wisdom in their academics. The emergence of nonlinear technology seems to be one such revolution. In a shocking demeanour, this new technology has disclosed a few misconceptions in our conventional knowing of determinism. particularly, it's been proven that the idea of predictability, in response to which the trajectory of a method will be accurately decided if one understands the equations of movement and the preliminary stipulations, is expounded to textbook examples of straightforward; integrable structures. This predictability doesn't expand to nonlinear, conservative structures commonly. Dissipative platforms may also express unpredictability, only if the movement is continued via externally provided power and/or assets. those discoveries, and the linked discovery that even fairly basic nonlinear structures can express tremendous complicated habit, have caused an unparalleled feeling of universal curiosity between scientists from many alternative disciplines. over the last decade or now we have come to appreciate that there are common routes to chaos, we've realized approximately stretching and folding, and now we have found the attractive fractal geometry underlying chaotic attractors.
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Extra resources for Complexity, Chaos, and Biological Evolution (Nato Science Series B:) (Volume 270)
Subharmonic bifurcations and chaotic episodes are clearly visible. irn [m~; 1 Figure 2. Cry segment with a sudden transition from a ''basic cry" (pitch about 400 Hz) to a subharmonic regime with nearly the double pitch period. 44 time [ms] Figure 3. Newborn cry displaying a transition to very low fundamental frequencies. octave jumps but also changes of the pitch by a factor of 3 are reported (Howard 1989). Another common phenomenon in speech is very low-pitched regimes (Dolansky and Tjerlund 1968, Catford 1977).
And Babloyantz, A. Predictability of human EEG: a dynamical approach. BioI. Cybernetics, in press, 1990. A. Intrinsic limits on dimension calculations. Phys. Lett. A. 133: 283288, 1988. 40 CHAOS AND BIFURCATIONS DURING VOICED SPEECH Hanspeter Herzel, Ina Steinecke, Werner Mende and Kathleen Wermke Humboldt University Berlin Invalidenstr. 42 1040 Berlin Federal Republic of Germany ABSTRACT Paralysis, laryngitis, cancer and other pathological conditions often lead to irregularities in the sounds of speech.
Then a backward octave jump to fast oscillations occurs. Comparable frequency breaks are observed also during human speech (Bowler 1964). -g-'••--, • , 1 11 .. , • I t 'I ,l1li I' U U I" " III: 2 Figure 1. Spectrogram from a premature infant (28 weeks) with respiratory complications. Subharmonic bifurcations and chaotic episodes are clearly visible. irn [m~; 1 Figure 2. Cry segment with a sudden transition from a ''basic cry" (pitch about 400 Hz) to a subharmonic regime with nearly the double pitch period.