By Teresa Ree Chay (auth.), Hans G. Othmer (eds.)
This quantity comprises the court cases of a gathering entitled 'Nonlinear Oscillations in Biology and Chemistry', which used to be held on the college of Utah could 9-11,1985. The papers fall into 4 significant different types: (i) those who care for organic difficulties, quite difficulties bobbing up in phone biology, (ii) those who care for chemical platforms, (iii) those who deal with difficulties which come up in neurophysiology, and (iv), these whose fundamental emphasis is on extra basic types and the mathematical recommendations all for their research. apart from the paper through Auchmuty, all are according to talks given on the assembly. the range of papers offers a few indication of the scope of the assembly, however the published observe conveys neither the measure of interplay among the contributors nor the highbrow sparks generated via that interplay. The assembly used to be made attainable through the monetary help of the dep. of Mathe matics of the collage of Utah. i'm indebted to Ms. Toni Bunker of the dept of arithmetic for her very capable help on all demeanour of information linked to the association of the assembly. eventually, a note of due to all members for his or her con tributions to the luck of the assembly, and to the individuals to this quantity for his or her efforts in getting ready their manuscripts.
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Additional info for Nonlinear Oscillations in Biology and Chemistry: Proceedings of a meeting held at the University of Utah, May 9–11, 1985
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Kopell. Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM J. Applied Math. (in press). 33 9. FitzHugh, R. 1961. Impulses and physiological states in models of nerve membrane. Biophys. J. 1 :445-466. 10. Hindmarsh, J. L~, and R. M. Rose. 1984. A model of neuronal bursting using three coupled first order differential equations. Proc. R. Soc. Lond. B ~:87-102. 11. Hodgkin, A. , and A. F. Huxley. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve.
Biosci. M. R. Klevecz: in Biomathematic~and Cell Kinetics (ed. M. Rotenberg), Elsevier/North Holland, Amsterdam-New York, 1981, p. 329. C. Mackey: in Temporal Order (eds. L. I. Jaeger), Springer-Verlag, Berlin-New York, 1985, p. 315 J. Engelberg: J. theor. Biol. M. Mitchinson: The Biology or-the Cell Cycle, Cambridge University Press, London-New York, 1913 A. C. Mackey: Probabilistic Behavior in Deterministic Systems, Cambridge University Press, London-New York, ln press 1985 A. A. Yorke: Rend.
We have contrasted in mathematical terms some of the differences between the two models. The fast subsystem of the Chay-Keizer model exhibits hysteresis (coexistence of a stable steady state and a stable oxcillation) while the Plant model does not. Without this hysteresis the Chay-Keizer model would not exhibit robust bursting for any parameter values of the slow subsystem; there would be no mechanism to sweep the single slow variable Ca into and out of the spike-oscillation mode. Therefore, by ad- justing slow-system parameters alone it is not possible to obtain a non-spiking slow wave with this model.