From Clocks to Chaos: The Rhythms of Life

Front Cover
Princeton University Press, Jul 21, 1988 - Mathematics - 248 pages

In an important new contribution to the literature of chaos, two distinguished researchers in the field of physiology probe central theoretical questions about physiological rhythms. Topics discussed include: How are rhythms generated? How do they start and stop? What are the effects of perturbation of the rhythms? How are oscillations organized in space? Leon Glass and Michael Mackey address an audience of biological scientists, physicians, physical scientists, and mathematicians, but the work assumes no knowledge of advanced mathematics.


Variation of rhythms outside normal limits, or appearance of new rhythms where none existed previously, are associated with disease. One of the most interesting features of the book is that it makes a start at explaining "dynamical diseases" that are not the result of infection by pathogens but that stem from abnormalities in the timing of essential functions. From Clocks to Chaos provides a firm foundation for understanding dynamic processes in physiology.

 

Contents

The Rhythms of Life
3
xi
13
Steady States Oscillations and Chaos
19
Noise and Chaos
36
Initiation and Termination of Biological Rhythms
82
Single Pulse Perturbation of Biological Oscillators
98
19
139
Spatial Oscillations
144
Mathematical Appendix
183
22
193
36
200
References
211
47
213
Mathematical Models for Biological Oscillators
221
Subject Index
243
Copyright

Dynamical Diseases
172

Other editions - View all

From Clocks to Chaos: The Rhythms of Life
Leon Glass,Michael C. Mackey
Limited preview - 2020
From Clocks to Chaos: The Rhythms of Life
Leon Glass,Michael C. Mackey
Limited preview - 1988
From Clocks to Chaos: The Rhythms of Life
Leon Glass,Michael C. Mackey
No preview available - 1988

Common terms and phrases

action potential alternans amplitude analysis annihilation Arnold tongues arrhythmias atrial beats behavior Belousov-Zhabotinsky reaction biological oscillators blood cardiac cells chaos chaotic dynamics chapter Cheyne-Stokes respiration circadian rhythm circle maps circus movement clinical complex compute cycle length delivered differential equations dimension discussed dynamical disease ectopic entrainment example experimental fibrillation finite difference equations fire models frequency function Glass Guevara heart Hopf bifurcation increases inhibitory initial conditions integrate and fire Jalife limit cycle limit cycle oscillation Mackey Math mathematical models mechanical ventilator membrane msec neural neurons normal observed orbit parameters parasystole patients period-doubling bifurcations periodic stimulation periodically forced phase locking phase plane phase resetting Physiol physiological rhythms Poincaré Poincaré map Poisson process possible Purkinje fiber respiration rhythmogenesis Rinzel shown in figure shows Shrier solution spiral waves squid giant axon stable limit cycle stable steady stimulus studies theoretical threshold tion tissue topological unstable values variables ventricular Winfree

Bibliographic information

TitleFrom Clocks to Chaos: The Rhythms of Life
Princeton paperbacks
AuthorsLeon Glass, Michael C. Mackey
Editionillustrated
PublisherPrinceton University Press, 1988
ISBN0691084963, 9780691084961
Length248 pages
Subjects ›  ›  › 

Mathematics / Applied
Science / Chaotic Behavior in Systems
Science / Life Sciences / Anatomy & Physiology
Science / Life Sciences / Biology
Science / Life Sciences / Zoology / General
  
Export CitationBiBTeX EndNote RefMan