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Department of Engineering
Mathematics Final Year Project: Influence of Stable Manifolds in Phase-Resetting of Excitable Cells by Siti Hasmah Mazlan Supervisors: Dr Hinke Osinga and Dr Krasimira Tsaneva-Atanasova |
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1 - Home 2 - Cell Model 3 - Bifurcation Analysis 4 - Stable Manifolds 5 - Phase-resetting 6 - References |
References Main Mazlan S.H., “Influence of stable manifolds in phase-resetting of excitable cells ”, project thesis submitted in support of the degree of Master of Engineering (MEng), Engineering Mathematics, University of Bristol, June 2008 Tsaneva-Atanasova K., Sherman A., van Goor F., Stojilkovic S.S., “Mechanism of spontaneous and receptor-controlled electrical activity in pituitary”, Journal of Neurophysiology, 98, pp. 131–144, 2007 Further Reading Cuthbertson R.,Holcombe M., Paton R., Computation in Cellular and Molecular Biological Systems, World Scientific Publishing, 1996 Deininger M., “Cell cycle and growth control: Current clinical applications”, In: Cell Cycle and Growth Control: Biomolecular Regulation and Cancer, (Eds) Stein G. S., Pardee A.B., Wiley IEEE, 2, pp. 669-706, 2004 Doedel E. J., “AUTO: a program for the automatic bifurcation analysis of autonomous systems”, Congressus Numerantium, 30, pp. 265-284, 1981 Ermentrout G.B., Simulating, Analyzing, and Animating Dynamical Systems: A Guide to Xppaut for Researchers and Students, SIAM Books, 2002 Hanselman D., Littlefield B., International edition: Mastering MATLAB 7, Pearson Education International, 2005 Hodgkin A., Huxley A., “A quantitative description of membrane current and its application to conduction and excitation in nerve”, Journal of Neurophysiology, 117, pp. 500-544, 1952 Kaplan D., Glass L., Understanding Nonlinear Dynamics, Birkhauser, pp. 37-40, 1995 Keener J.P., Sneyd J., Mathematical Physiology, Springer, 1987 Kuznetsov Y.A., Elements of Applied Bifurcation Theory, Springer, pp. 316–326, 2004 Raina A.K., Zhu X., Mervyn M., Takeda A., Smith M.A. , “Abortive oncogeny and cell cycle-mediated events in Alzheimer disease”, In: Progress in Cell Cycle Research, (Eds) Meijer L., Jézéquel A., Ducommon B., Kluwer Academic/Plenum Publisher, New York, 4, pp. 235-242, 2000 Rinzel, J., “Bursting oscillations in an excitable membrane model”, In: Ordinary and Partial Differential Equations, (Eds) Sleeman B.D. & Jarvis R.J. , Springer-Verlag, New York, 1151, pp. 68-88, 1985 Stern J.V., Osinga H.M., LeBeau A., Sherman A., “Resetting behavior in a model of bursting in secretory pituitary cells: Distinguishing plateaus from pseudo-plateaus”, Bulletin of Mathematical Biology, 70(1), pp. 68-88, 2008 Strogatz, S.H., Nonlinear dynamics and chaos: With applications to physics, biology, chemistry and engineering, Perseus Publishing, 2001 Winfree A.T., When Time Breaks Down, Princeton University Press, Princeton, 1897 |
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