From cell division to heartbeat, clocklike rhythms pervade the activities of every living organism. The cycles of life are ultimately biochemical in mechanism but many of the principles that dominate their orchestration are essentially mathematical.The Geometry of Biological Time describes periodic processes in living systems and their non-living analogues in the abstract terms of nonlinear dynamics. Enphasis is given in phase singularities, waves, and mutual synchronization in tissues composed of many clocklike units. Also provided are descriptions of the best-studied experimental systems such as chemical oscillators, pacemaker neurons, circadian clocks, and excitable media organized into biochemical and bioelectrical wave patterns in two and three dimensions.No theoretical background is assumed; the required notions are introduced through an extensive collection of pictures and easily understood examples.This extensively updated new edition incorporates the fruits of two decades' further exploration guided by the same principles. Limit cycle theories of circadian clocks are now applied to human jet lag and are understood in terms of the molecular genetics of their recently discovered mechanisms. Supercomputers reveal the unforeseen architecture and dynamics of three-dimensional scroll waves in excitable media. Their role in life-threatening electrical aberrations of the heartbeat is exposed by laboratory experiments and corroborated in the clinic. These developments trace back to three basic mathematical ideas.

This second edition of a classic mathematical biology book deals with the dynamics of processes that repeat themselves regularly. This cycle of change is a ubiquitous principle of organization in living systems. This new edition addresses areas in biomathematics that have come to fruition since 1980. The author, a leader in the field, offers valuable insights into the important areas of future development in nonlinear dynamics in the natural sciences.

Dealing with dynamics of processes that repeat themselves regularly, this revised and updated edition extends the thread from 1980 to the new millennium, concentrating on areas of interest where there should be much activity in the future.

Geometry of Biological Time deals with dynamics of processes that repeat themselves regularly. Such rhythmic return through a cycle of change is an ubiquitous principle of organization in living systems. In this revised and updated edition the author plans to extend the thread from 1980 to the present concentrating on areas which he personally feels have been interesting and where he feels there will be much activity in the future. This involves going through spatial biochemical, electrophysiological, and organismic dynamical systems and patterns that were discovered by pursuing the theme of phase singularities that the original book introduced. In particular the work on excitability in cell membranes has been thoroughly updated as have the references throughout the book.

Includes bibliographical references (p. 661-758) and indexes.

Introduction.- Circular Logic.- Phase Singularities (Screwy Results of Circular Logic).- The Rules of the Ring.- Ring Populations.- Getting Off the Ring.- Attracting Cycles and Isochrons.- Measuring the Trajectories of a Circadian Clock.- Populations of Attractor Cycle Oscillators.- Excitable Kinetics and Excitable Media.- The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways.- The Firefly Machine.- Energy Metabolism in Cells.- The Malonic Acid Reagent ("Sodium Geometrate").- Electrical Rhythmicity and Excitability in Cell Membranes.- The Aggregation of Slime Mold Amoebae.- Growth and Regeneration.- Arthropod Circle.- Pattern Formation in the Fungi.- Circadian Rhythms in General.- The Circadian Clocks of Insect Eclosion.- The Flower of Kalanchoe.- The Cell Mitotic Cycle.- The Female Cycle.- References.- Index of Names.- Index of Subjects.