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Electrical activities of insulin secretion in pancreatic islets are characterized by bursts of action potentials. With a simple but representative Vries-Sherman model, we determine the regions of different types of bursting in two-parameter plane through the two-parameter bifurcation analysis of the fast subsystem. Moreover, fast/slow analysis is used to reveal topological types of bursting patterns for different values of the parameter Vm and transition mechanisms between them.
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Keywords:
- bursting /
- fast/slow analysis /
- codimension-2 bifurcation
[1] Chou H F, Ipp E 1990 Diabetes 39 112
[2] [3] Longo E A, Tornheim K, Deeney J T, Varnum B A, Tillotson D, Prentki M, Corkey B E 1991 J. Biol. Chem. 266 9314
[4] Omeara N M, Sturis J, Blackman J D, Byrne M M, Jaspan J B, Thistlethwaite J R, Polonsky K S 1993 Diabetes 42 855
[5] [6] Bertram R, Butte M J, Kiemel T and Sherman A 1995 Bull. Math. Biol. 57 413
[7] [8] [9] Rinzel J 1987 Lecture Notes in Biomathematics (New York: Springer-Verlag) p267
[10] Izhikevich E M 2000 Int. J. Bifur. and Chaos 10 1171
[11] [12] [13] Gao Z Y, Lu Q S 2007 Chin. Phys. 16 2479
[14] [15] Yang Z Q, Lu Q S 2006 Chin. Phys. 15 518
[16] [17] Xie Y, Xu J X, Kang Y M, Hu S J, Duan Y B 2003 Acta Phys. Sin. 52 1112 (in Chinese)[谢 勇、徐健学、康艳梅、胡三觉、段玉斌 2003 52 1112]
[18] Wu Y, Xu J X, He D H, Jin W Y 2005 Acta Phys. Sin. 54 3457(in Chinese)[吴 莹、徐健学、何岱海、靳伍银 2005 54 3457]
[19] [20] Wang B Y, Xu W, Xing Z C 2009 Acta Phys. Sin. 58 6590(in Chinese)[王宝燕、徐 伟、邢真慈 2009 58 6590]
[21] [22] Chay T R, Keizer J 1983 Biophys J. 42 181
[23] [24] Atwater I, Dawson C M, Scott A, Eddlestone G, Rojas E 1980 Biochemistry and Biophysics of the Pancreatic -cell Thieme G (Ed) (New York: Verlag) p100
[25] [26] [27] Keizer J, Smolen P 1991 Proc. Natl. Acad. Sci. USA 88 3897
[28] [29] Keizer J, Magnus G 1989 Biophys. J. 56 229
[30] [31] Vries G D, Sherman A 2000 J. Theor. Biol. 207 513
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[1] Chou H F, Ipp E 1990 Diabetes 39 112
[2] [3] Longo E A, Tornheim K, Deeney J T, Varnum B A, Tillotson D, Prentki M, Corkey B E 1991 J. Biol. Chem. 266 9314
[4] Omeara N M, Sturis J, Blackman J D, Byrne M M, Jaspan J B, Thistlethwaite J R, Polonsky K S 1993 Diabetes 42 855
[5] [6] Bertram R, Butte M J, Kiemel T and Sherman A 1995 Bull. Math. Biol. 57 413
[7] [8] [9] Rinzel J 1987 Lecture Notes in Biomathematics (New York: Springer-Verlag) p267
[10] Izhikevich E M 2000 Int. J. Bifur. and Chaos 10 1171
[11] [12] [13] Gao Z Y, Lu Q S 2007 Chin. Phys. 16 2479
[14] [15] Yang Z Q, Lu Q S 2006 Chin. Phys. 15 518
[16] [17] Xie Y, Xu J X, Kang Y M, Hu S J, Duan Y B 2003 Acta Phys. Sin. 52 1112 (in Chinese)[谢 勇、徐健学、康艳梅、胡三觉、段玉斌 2003 52 1112]
[18] Wu Y, Xu J X, He D H, Jin W Y 2005 Acta Phys. Sin. 54 3457(in Chinese)[吴 莹、徐健学、何岱海、靳伍银 2005 54 3457]
[19] [20] Wang B Y, Xu W, Xing Z C 2009 Acta Phys. Sin. 58 6590(in Chinese)[王宝燕、徐 伟、邢真慈 2009 58 6590]
[21] [22] Chay T R, Keizer J 1983 Biophys J. 42 181
[23] [24] Atwater I, Dawson C M, Scott A, Eddlestone G, Rojas E 1980 Biochemistry and Biophysics of the Pancreatic -cell Thieme G (Ed) (New York: Verlag) p100
[25] [26] [27] Keizer J, Smolen P 1991 Proc. Natl. Acad. Sci. USA 88 3897
[28] [29] Keizer J, Magnus G 1989 Biophys. J. 56 229
[30] [31] Vries G D, Sherman A 2000 J. Theor. Biol. 207 513
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