Nonlinear Oscillations in Biology and Chemistry

1. Front Matter

   Pages I-VI

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2. Biological Systems

   1. Front Matter

      Pages 1-1

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   2. Oscillations and Chaos in the Pancreatic β-Cell

      • Teresa Ree Chay

      Pages 2-18

   3. On Different Mechanisms for Membrane Potential Bursting

      • John Rinzel, Young Seek Lee

      Pages 19-33

   4. A Mitotic Oscillator with a Strange Attractor and Distributions of Cell Cycle Times

      • Michael C. Mackey, Martin Santavy, Pavla Selepova

      Pages 34-45

   5. An Analysis of One- and Two-Dimensional Patterns in a Mechanical Model for Morphogenesis

      • P. K. Maini, J. D. Murray, G. F. Oster

      Pages 46-65

3. Chemical Systems

   1. Front Matter

      Pages 67-67

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   2. Electrically Coupled Belousov-Zhabotinskii Oscillators: Experimental Observation of Chaos in a Chemical System and Identification of its Source in the Field-Noyes Equations

      • Michael F. Crowley, Richard J. Field

      Pages 68-97

   3. Losing Amplitude and Saving Phase

      • Bard Ermentrout

      Pages 98-114

   4. Spiral Waves in Excitable Media

      • James P. Keener

      Pages 115-127

4. Neurophysiology

   1. Front Matter

      Pages 129-129

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   2. Biomechanical and Neuromotor Factors in Mammalian Locomotor-Respiratory Coupling

      • D. M. Bramble

      Pages 130-149

   3. Analysis of a VCON Neuromime

      • F. C. Hoppensteadt

      Pages 150-159

   4. Coupled Oscillators and Locomotion by Fish

      • N. Kopell

      Pages 160-174

   5. Experimental Studies of Chaotic Neural Behavior: Cellular Activity and Electroencephalographic Signals

      • P. E. Rapp, I. D. Zimmerman, A. M. Albano, G. C. deGuzman, N. N. Greenbaun, T. R. Bashore

      Pages 175-205

5. Mathematical Methods

   1. Front Matter

      Pages 207-207

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   2. A Period-Doubling Bubble in the Dynamics of Two Coupled Oscillators

      • J. C. Alexander

      Pages 208-220

   3. Bistable Behavior in Coupled Oscillators

      • D. G. Aronson, E. J. Doedel, H. G. Othmer

      Pages 221-231

   4. Continuation of Arnold Tongues in Mathematical Models of Periodically Forced Biological Oscillators

      • Leon Glass, Jacques Bélair

      Pages 232-243

   5. Averaging and Synchronization of Weakly Coupled Systems

      • Humberto Carrillo Calvet

      Pages 244-251

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.

• Diffusion
• biology
• distribution
• numerical analysis
• physiology

• Department of Mathematics, University of Utah, Salt Lake City, USA

  Hans G. Othmer

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