By Erik Mosekilde, Lis Mosekilde
From time to time, maybe a couple of times each one century, a revolution happens that questions a few of our simple ideals and sweeps throughout another way good guarded disciplinary barriers. those are the sessions whilst technology is enjoyable, whilst new paradigms need to be formulated, and while younger scientists can do severe paintings with out first having to obtain the entire wisdom in their lecturers. The emergence of nonlinear technology seems to be one such revolution. In a shocking demeanour, this new technological know-how has disclosed a few misconceptions in our conventional knowing of determinism. specifically, it's been proven that the idea of predictability, in keeping with which the trajectory of a procedure should be accurately made up our minds if one is familiar with the equations of movement and the preliminary stipulations, is expounded to textbook examples of straightforward; integrable platforms. This predictability doesn't expand to nonlinear, conservative structures as a rule. Dissipative platforms may also convey unpredictability, only if the movement is continued through externally provided strength and/or assets. those discoveries, and the linked discovery that even particularly easy nonlinear platforms can exhibit tremendous advanced habit, have led to an remarkable feeling of universal curiosity between scientists from many alternative disciplines. over the past decade or we now have come to appreciate that there are common routes to chaos, we've got discovered approximately stretching and folding, and we now have stumbled on the attractive fractal geometry underlying chaotic attractors.
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Extra info for Complexity, Chaos, and Biological Evolution
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.
The results are compared with the same quantities obtained this time from the evaluation of the spectrum of Lyapounov exponent following Kaplan York and Mori conjectures [11, 12]. With the use of recurrence plots it is also shown how to assess the stationarity of time series. The latter technique may reveal the presence of hidden periodicities of longer wave length superimposed on otherwise chaotic dynamics. 2 Stationarity of time series Recently Eckman and colleagues  proposed a novel, elegant graphical tool, called a "recurrence plot" for the diagnoses of the presence of drift and hidden periodicities in the time evolution of dynamical systems which are unnoticeable otherwise.
Editorial: Tetracycline Based Histological Analysis of Bone Remodeling", Calif. Tissue Res. : "The Skeletal Intermediary Organization", Metab. Bone Dis. Relat. Res. -H. P. Leyssac: IITGF- Mediated Oscillations in the Proximal Intratubular Pressure: Differences between Spontaneously Hypertensive Rats and Wistar-Kyoto Rats", Acta Physiol. Scand. -H. P. Leyssac: IIOscillations in the Proximal Intratubular Pressure: A Mathematical Modelll, Am. J. Physiol. , E. -H. Holstein-Rathlou: IISelf-Sustained Oscillations and Chaotic Behavior in Kidney Pressure Regulationll, Proc.