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


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