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Hopf bifurcation in a calcium oscillation model and its control: frequency domain approach. (English) Zbl 1270.34120

Summary: The Hopf bifurcation in a calcium oscillation model is theoretically analyzed by Hopf bifurcation theory in frequency domain. Approximation expressions for frequencies and amplitudes of periodic orbits arising from Hopf bifurcation are provided by using second-order harmonic balance method. In addition, a new method is proposed to control the amplitudes of the periodic orbits. Numerical simulations show the effectiveness of the method for suppressing periodic oscillations.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
92C37 Cell biology
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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[1] DOI: 10.1038/361315a0 · doi:10.1038/361315a0
[2] DOI: 10.1038/27094 · doi:10.1038/27094
[3] DOI: 10.1016/S0301-4622(97)00010-0 · doi:10.1016/S0301-4622(97)00010-0
[4] DOI: 10.1038/31960 · doi:10.1038/31960
[5] DOI: 10.1016/0143-4160(93)90052-8 · doi:10.1016/0143-4160(93)90052-8
[6] DOI: 10.1101/cshperspect.a004226 · doi:10.1101/cshperspect.a004226
[7] Farooqi A. A., Int. J. Bioautomat. 14 pp 233– (2010)
[8] DOI: 10.1006/bulm.1999.0095 · Zbl 1323.92085 · doi:10.1006/bulm.1999.0095
[9] DOI: 10.1109/TCSI.2002.802348 · Zbl 1368.34043 · doi:10.1109/TCSI.2002.802348
[10] DOI: 10.1016/S0006-3495(00)76373-9 · doi:10.1016/S0006-3495(00)76373-9
[11] DOI: 10.1038/31965 · doi:10.1038/31965
[12] DOI: 10.1109/TCS.1979.1084636 · Zbl 0438.93035 · doi:10.1109/TCS.1979.1084636
[13] DOI: 10.1109/9.277247 · Zbl 0800.93536 · doi:10.1109/9.277247
[14] DOI: 10.1007/s00360-008-0331-3 · doi:10.1007/s00360-008-0331-3
[15] Nicola I. R., ROMAI J. 2 pp 157– (2006)
[16] DOI: 10.1016/S0960-0779(03)00027-4 · Zbl 1068.92017 · doi:10.1016/S0960-0779(03)00027-4
[17] Puebla H., Chinese Contr. Decis. Conf. pp 4309– (2008)
[18] DOI: 10.1046/j.0014-2956.2001.02720.x · doi:10.1046/j.0014-2956.2001.02720.x
[19] DOI: 10.1016/S0009-2614(01)00625-X · doi:10.1016/S0009-2614(01)00625-X
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