Titlebook: Mathematics as a Laboratory Tool; Dynamics, Delays and John Milton,Toru Ohira Textbook 2021Latest edition Springer Nature Switzerland AG 20

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Equilibria and Steady States,Mathematical models of dynamical systems often take the general form where the . are the variables and the . describe the interactions between variables. From the perspective of (.), the goal of science is to identify the . and the form of the functions ..

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Stability,A reasonable starting point for the study of input–output relationships is to assume that the black box shown in Figure . contains a dynamical system operating at its fixed point. In a laboratory setting, this is equivalent to a system that is either at equilibrium or in a steady state.

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Feedback and Control Systems,One of the most important regulatory mechanisms is feedback [24, 37]. Virtually, every physiological variable is associated with a feedback control loop. Indeed, some would even say that every such variable has multiple feedback loops associated with it [35, 277].

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Characterizing and Manipulating Oscillations,Oscillations are characterized by their amplitudes and frequency content. As we saw in Section ., determination of the power spectrum is a powerful technique to describe oscillations. In chronobiology, circadian rhythms are fit to a sinusoid with period 24 hours using cosinor analysis [146].

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Noisy Dynamical Systems,While examining the form of these particles immersed in water, I observed many of them very evidently in motion. These motions were such to satisfy me that they arose neither from currents in the field, nor from its gradual evaporation, but belonged to the particle itself.

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Random Walks,We began this book with the notion that the mechanisms that underlie biological processes are deterministic. This hypothesis underscores the use of models based on ordinary and delay differential equations. Then, in the last two chapters, we admitted the possibility that there is likely to be a stochastic (random) element as well.

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r, the finite element-discrete variable representation (introduced in Chap. .) is used and demonstrates its benefits regarding the two-time solution of the Kadanoff-Baym equations. Moreover, the NEGF results are supplemented by thorough comparisons to exact diagonalization and solutions of the time-

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John Milton,Toru Ohirafect. The chemical energy released during the association of superequilibrium atomic hydrogen changed graphite from a stable phase into a metastable phase, while diamond became a stable phase. That was the reason why diamond can grow steadily at activated low pressures.