By Teresa Ree Chay (auth.), Hans G. Othmer (eds.)
This quantity includes the court cases of a gathering entitled 'Nonlinear Oscillations in Biology and Chemistry', which was once held on the collage of Utah might 9-11,1985. The papers fall into 4 significant different types: (i) those who take care of organic difficulties, quite difficulties bobbing up in phone biology, (ii) those who take care of chemical structures, (iii) those who deal with difficulties which come up in neurophysiology, and (iv), these whose basic emphasis is on extra common types and the mathematical recommendations excited by their research. aside from the paper by means of 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 note conveys neither the measure of interplay among the individuals nor the highbrow sparks generated by means of that interplay. The assembly used to be made attainable by way of the monetary help of the dept of Mathe matics of the college 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 notice of due to all members for his or her con tributions to the luck of the assembly, and to the members to this quantity for his or her efforts in getting ready their manuscripts.
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Additional resources for Nonlinear Oscillations in Biology and Chemistry: Proceedings of a meeting held at the University of Utah, May 9–11, 1985
We proceed as in Section 2. First, if x is held fixed and Ca is considered as a parameter then the fast subsystem has solutions with a bifurcation structure (Fig. 5) which appears not unlike that shown in Fig. 2. A noticeable quantitative difference is that here the homoclinic orbit occurs (to the accuracy of our numerical calculations) at the coalescence of two steady states. ) This means that if Ca were swept very slowly back and forth across CaHC the fast system would switch between the repetitive firng mode and the steady state mode but without exhibiting any hystersis beI havior.
14. Plant, R. , and M. Kim. 1976. Mathematical description of a bursting pacemaker neuron by a modification of the Hodgkin-Huxley equations. Biophys. J. 16:227-244. 15. Plant, R. E. 1981. Bifurcation and resonance in a model for bursting nerve cells. J. Math. Biology 11 :15-32. 16. , and W. C~Troy. 1982. Bursting phenomena in a simplified Oregonator flow system model. J. Chem. Phys. 76:1775-1789. 17. Rinzel, J. Bursting oscillations in an excitable membrane model. In Proc. 8th Dundee Conf. , B.
F. Huxley. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (Lond) 117:500-544. , G. Mutschler, and R. Seitz. 1985. Coupling of a slow and a fast oscillator can generate bursting. Bull. Math. BioI. 47:1-21. 13. Nagumo, J. , S. Arimoto, and S. Yoshizawa. 19t1:2. An active pulse transmission line simulating nerve axon. Proc. IRE. 50:2061-2070. 14. Plant, R. , and M. Kim. 1976. Mathematical description of a bursting pacemaker neuron by a modification of the Hodgkin-Huxley equations.