Nonlinear Oscillations in Biology and Chemistry

This volume contains the proceedings of a meeting entitled 'Nonlinear Oscillations in Biology and Chemistry', which was held at the University of Utah May 9-11,1985. The papers fall into four major categories: (i) those that deal with biological problems, particularly problems arising in cell biology, (ii) those that deal with chemical systems, (iii) those that treat problems which arise in neurophysiology, and (iv), those whose primary emphasis is on more general models and the mathematical techniques involved in their analysis. Except for the paper by Auchmuty, all are based on talks given at the meeting. The diversity of papers gives some indication of the scope of the meeting, but the printed word conveys neither the degree of interaction between the participants nor the intellectual sparks generated by that interaction. The meeting was made possible by the financial support of the Department of Mathe matics of the University of Utah. I am indebted to Ms. Toni Bunker of the Department of Mathematics for her very able assistance on all manner of details associated with the organization of the meeting. Finally, a word of thanks to all participants for their con tributions to the success of the meeting, and to the contributors to this volume for their efforts in preparing their manuscripts.

Biological Systems.- Oscillations and Chaos in the Pancreatic ?-Cell.- On Different Mechanisms for Membrane Potential Bursting.- A Mitotic Oscillator with a Strange Attractor and Distributions of Cell Cycle Times.- An Analysis of One- and Two-Dimensional Patterns in a Mechanical Model for Morphogenesis.- Chemical Systems.- Electrically Coupled Belousov-Zhabotinskii Oscillators: Experimental Observations of Chaos in a Chemical System and Identification of Its Source in the Field-Noyes Equations.- Losing Amplitude and Saving Phase.- Spiral Waves in Excitable Media.- Neurophysiology.- Biomechanical and Neuromotor Factors in Mammalian Locomotor-Respiratory Coupling.- Analysis of a VCON Neuromime.- Coupled Oscillators and Locomotion by Fish.- Experimental Studies of Chaotic Neural Behavior: Cellular Activity and Electroencephalographic Signals.- Mathematical Methods.- A Period-Doubling Bubble in the Dynamics of Two Coupled Oscillators.- Bistable Behavior in Coupled Oscillators.- Continuation of Arnold Tongues in Mathematical Models of Periodically Forced Biological Oscillators.- Averaging and Synchronization of Weakly Coupled Systems.- Variational Principles for Periodic Solutions of Autonomous Ordinary Differential Equations.- A Numerical Analysis of Wave Phenomena in a Reaction Diffusion Model.- On a Nonlinear Hyperbolic Equation Describing Transmission Lines, Cell Movement, and Branching Random Walks.