The Geometry of Biological Time

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.

This is an update of a classic mathematical biology book by an author who is a leader in the field. It deals with dynamics of processes that repeat themselves regularly. This cycle of change is an ubiquitous principle of organization in living systems. In this new edition the author addresses areas that have come to fruition since 1980 and also concentrates on areas which he personally feels will see much activity in future.

1. Circular Logic.- 2. Phase Singularities (Screwy Results of Circular Logic).- 3. The Rules of the Ring.- 4. Ring Populations.- 5. Getting off the Ring.- 6. Attracting Cycles and Isochrons.- 7. Measuring the Trajectories of a Circadian Clock.- 8. Populations of Attracting-Cycle Oscillators.- 9. Excitable Kinetics and Excitable Media.- 10. The Varieties of Phaseless Experience: In which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways.- 11. The Firefly Machine.- 12. Energy Metabolism in Cells.- 13. The Malonic Acid Reagent ("Sodium Geometrate").- 14. Electrical Rhythmicity and Excitability in Cell Membranes.- 15. The Aggregation of Slime Mold Amoebae.- 16. Numerical Organizing Centers.- 17. Electrical Singular Filaments in the Heart Wall.- 18. Pattern Formation in the Fungi.- 19. Circadian Rhythms in General.- 20. The Circadian Clocks of Insect Eclosion.- 21. The Flower of Kalanchoë.- 22. The Cell Mitotic Cycle.- 23. The Female Cycle 650 A: Women, Hormones, and Eggs.- Index of Author Citations and Publications.- Index of Subjects.