Complexity, Chaos, and Biological Evolution by Erik Mosekilde, Lis Mosekilde

By Erik Mosekilde, Lis Mosekilde

From time to time, probably a couple of times every one century, a revolution happens that questions a few of our uncomplicated ideals and sweeps throughout another way good guarded disciplinary barriers. those are the sessions while technological know-how is enjoyable, whilst new paradigms must be formulated, and whilst younger scientists can do critical paintings with no first having to procure the entire wisdom in their lecturers. The emergence of nonlinear technological know-how seems to be one such revolution. In a stunning demeanour, this new technology has disclosed a couple of misconceptions in our conventional figuring out of determinism. particularly, it's been proven that the idea of predictability, in accordance with which the trajectory of a procedure will be accurately decided if one is familiar with the equations of movement and the preliminary stipulations, is said to textbook examples of easy; integrable structures. This predictability doesn't expand to nonlinear, conservative platforms ordinarily. Dissipative platforms may also exhibit unpredictability, only if the movement is continued through externally provided power and/or assets. those discoveries, and the linked discovery that even really uncomplicated nonlinear platforms can express tremendous advanced habit, have led to an extraordinary feeling of universal curiosity between scientists from many alternative disciplines. over the last decade or we now have come to appreciate that there are common routes to chaos, now we have realized approximately stretching and folding, and we now have stumbled on the attractive fractal geometry underlying chaotic attractors.

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Cries are more or less unstationary processes. Transitions between several oscillatory modes occur very suddenly (in a few milliseconds). However, in many cases time segments of 5-20 ms can be considered as approximately stationary episodes and, therefore, time series analysis makes sense. The unstationarity of cries has the advantage that many changes (''bifurcations'') become visible during a single cry. In order to visualize the evolution of the spectral density during a cry, so-called spectrograms (or sonagrams) are appropriate.

I i 'Ii:: t! , t\ I, I~ II lI I 1 I ( I : : ( I I ! ·4 • I, 50 ",'. 1 \. ,;, • ! ms 100 Figure 4. Simulation of voiced sound. (a) Elongations xl and x 2 of the two masses (b) Volume velocity at the glottis (c) Mouth sound pressure a InS o 100 200 Figure 5. Toroidal oscillations leading to low pitched sound. f\ b , il. f'. I , I~ I " f', 1 . r: I ' \ " J:" c ms o 100 50 Figure 6. Entrainment of the two oscillators with a frequency ratio of 2:3. This resonance leads to an acoustic signal with a multiple period of normal voice as in Fig.

L. ): "Lectures in the Sciences of Complexity", Santa Fe Institute Studies in the Sciences of Complexity, Addison-Wesley, Redwood City (1988) References Anderson, RM. and RM. May: "Complex Dynamical Behavior in the Interaction between HIV and the Immune System", in "Cell to Cell Signalling", ed. A and RG. " Can. J. Spt. Sci. M. P. : "Editorial: Tetracycline Based Histological Analysis of Bone Remodeling", Calif. Tissue Res. : "The Skeletal Intermediary Organization", Metab. Bone Dis. Relat. Res.

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