Computer methods. Part A - download pdf or read online

By Michael L. Johnson, Ludwig Brand

ISBN-10: 0123745527

ISBN-13: 9780123745521

ISBN-10: 1865843830

ISBN-13: 9781865843834

The mix of speedier, extra complex pcs and extra quantitatively orientated biomedical researchers has lately yielded new and extra special equipment for the research of biomedical information. those larger analyses have stronger the conclusions that may be drawn from biomedical info, they usually have replaced the way in which that experiments are designed and played. This quantity, in addition to earlier and coming near near 'Computer equipment' volumes for the equipment in Enzymology serial, goals to notify biomedical researchers approximately contemporary functions of recent facts research and simulation tools as utilized to biomedical examine.

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If subsequent perturbations can be regarded as approximately independent, the associated phase response curve can be applied iteratively. Iterated maps allow us to generalize effects of single pulses to series of perturbations. For subsequent pulses we can apply the iterated map repeatedly and obtain in this way a series of phases {f0, f1, f2, . }. Along these lines, 1:1 entrainment can be related to the stable fixed point of the iterated map. 5. Entrainment zones and circle map As discussed earlier, two coupled oscillators can exhibit a variety of dynamics, ranging from synchronization with rational p:q frequency ratios to toroidal oscillations and deterministic chaos.

1998; Seidel and Herzel, 1998), meaning that there are four heart beats (oscillator 1) during one respiration cycle (oscillator 2). Prominent examples are the entrainment of autonomous circadian rhythms by the light– dark cycle (compare with Fig. , 1981). The latter example illustrates the complex dynamics of coupled oscillators: Apart from 1:1 frequency locking between external stimuli and internal beats, other entrainment ratios, such as 1:2, 2:3, and 3:2, can be detected. , 2000). , 1984).

They quantify the response of an oscillator to pulselike perturbations. Phase response curves provide valuable information on the properties of oscillators and their synchronization. 1016/S0076-6879(08)03801-9 # 2009 Elsevier Inc. All rights reserved. 1 2 A. Granada et al. ) in the context of nonlinear dynamics theory. Coupled oscillators can synchronize with different frequency ratios, can generate toroidal dynamics (superposition of independent frequencies), and may lead to deterministic chaos.

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