By George L. Gerstein (auth.), Frank H. Eeckman (eds.)
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This article presents the elemental ideas and strategies of genuine research for college students in all of those parts. It is helping one enhance the facility to imagine deductively, examine mathematical occasions and expand principles to a brand new context. just like the first 3 versions, this variation keeps an analogous spirit and elementary method with addition examples and enlargement on Logical Operations and Set idea.
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3). 5 Summary We have outlined theories to account for the generation and synchronization of bursting oscillations in an ensemble of electrically excitable cells. 8-cells) we have chosen for illustration. We have employed mathematical concepts that also apply more generally and which have enabled us to identify the underlying qualitative structure of a class of models. 41 An essential feature in this type of bursting model, made transparent by our fast/slow dissection and phase space representation, is bistability for the spike-generating subsystem.
Bangham, J. , and Rojas, E. (1984) Electrical coupling between cells in islets of Langerhans in mouse J. Membrane BioI. 77, 1-14. [91 FitzHugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1,445-466.  Gray, C. M. and Singer, W. (1989). Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proc. Nati. Acad. Sci. USA 86, 1698-1702.  Henquin, J. C. and Meissner, H. P. (1984). Significance of ionic ftuxes and changes in membrane potential for stimulus-secretion coupling in pancreatic B-cells.
To complete the graphical representation we indicate, with the curve labeled S = 0, the values of V and S where, according to Eqn. 3, the growth rate of S balances its decay; above the curve, S is increasing, and below it, decreasing. This curve is called the S-nullcline. As an application of this representation, consider our model for bursting in the ,8-cell and suppose that the calcium removal rate kCa is glucose-sensitive (say, increasing with glucose). This parameter appears only in the equation for the slow variable, Eqn.
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