Peter T. Saunders’s scientific contributions

The presented book is a corrected printing of the 1980-edition, see the review Zbl 0464.92001. It 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 particular, attention is drawn to phase singularities which play an important role in self-organization of biological patterns in space and time. Corresponding to the title “Geometry of biological time” rhythmic changes not in space so much as in time are studied. A phase singularity is a point (in the state space) at which phase is ambiguous and near which phase takes on all values. In chapter 2, examples of phase singularities, also of living clocks, are described and in chapter 10 the physical nature of phase singularities is discussed. The first part of the book (10 chapters) sketches on a lightly abstract level theoretical aspects of clocks (circular logic, phase singularities, rules of the ring, ring populations, collective rhythmicity, attracting cycles, circadian clock, attractor cycle oscillators, breakdown of rhythmic organization). Particular experimental systems described in the second half of the book provide background facts about the organisms or phenomena mentioned in the first half. The book is intended primarily for research students.