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Transition mechanisms of bursting in a two-cell network model of the pre-Bötzinger complex. (English) Zbl 1317.34101

Summary: Persistent sodium and calcium activated nonspecific cationic currents play important roles in the respiratory rhythm generation of the pre-Bötzinger complex. In this paper, we study the bursting patterns and their transition mechanisms in the two-parameter space of a two-cell network model of the pre-Bötzinger complex with synaptic coupling. Using the methods of fast/slow decomposition and two-parameter bifurcation analysis, we divide the two-parameter space into four different regions according to the multiphase oscillations, and reveal the possible transition mechanisms of bursting between these different regions. We also study the dynamics of the system with varying synaptic coupling strength. This work provides insights of how currents and synaptic coupling work on the respiratory rhythm generation.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
92C20 Neural biology
34E15 Singular perturbations for ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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References:

[1] DOI: 10.1137/050625540 · Zbl 1106.34023 · doi:10.1137/050625540
[2] Butera R. J., J. Neurophysiol. 82 pp 382– (1999)
[3] Butera R. J., J. Neurophysiol. 82 pp 398– (1999)
[4] DOI: 10.1113/jphysiol.2007.134577 · doi:10.1113/jphysiol.2007.134577
[5] DOI: 10.1152/jn.00081.2002 · doi:10.1152/jn.00081.2002
[6] DOI: 10.1016/S0896-6273(02)00712-2 · doi:10.1016/S0896-6273(02)00712-2
[7] DOI: 10.1006/bulm.2001.0228 · Zbl 1323.92079 · doi:10.1006/bulm.2001.0228
[8] DOI: 10.1142/S0218127412501143 · Zbl 1258.92009 · doi:10.1142/S0218127412501143
[9] DOI: 10.1007/s10827-010-0311-y · doi:10.1007/s10827-010-0311-y
[10] DOI: 10.1137/1.9780898718195 · Zbl 1003.68738 · doi:10.1137/1.9780898718195
[11] Gu H., Int. J. Bifurcation and Chaos 23 pp 1350195-1– (2013)
[12] DOI: 10.1016/j.physa.2012.11.049 · doi:10.1016/j.physa.2012.11.049
[13] DOI: 10.1142/S0218127400000840 · Zbl 1090.92505 · doi:10.1142/S0218127400000840
[14] DOI: 10.1111/ejn.12042 · doi:10.1111/ejn.12042
[15] DOI: 10.1088/1674-1056/23/5/050510 · doi:10.1088/1674-1056/23/5/050510
[16] DOI: 10.1007/978-1-4757-2421-9 · doi:10.1007/978-1-4757-2421-9
[17] DOI: 10.5772/13252 · doi:10.5772/13252
[18] DOI: 10.1113/jphysiol.2007.133660 · doi:10.1113/jphysiol.2007.133660
[19] DOI: 10.1113/jphysiol.2006.124602 · doi:10.1113/jphysiol.2006.124602
[20] DOI: 10.1007/s10827-012-0425-5 · Zbl 1276.92019 · doi:10.1007/s10827-012-0425-5
[21] DOI: 10.1038/nn1650 · doi:10.1038/nn1650
[22] DOI: 10.1523/JNEUROSCI.4238-04.2005 · doi:10.1523/JNEUROSCI.4238-04.2005
[23] DOI: 10.1007/BFb0074739 · doi:10.1007/BFb0074739
[24] DOI: 10.1073/pnas.0808776106 · doi:10.1073/pnas.0808776106
[25] DOI: 10.1046/j.1460-9568.2003.02739.x · doi:10.1046/j.1460-9568.2003.02739.x
[26] Shi X., Int. J. Bifurcation and Chaos 22 pp 1250101-1– (2012)
[27] DOI: 10.1126/science.1683005 · doi:10.1126/science.1683005
[28] Song Z., Int. J. Bifurcation and Chaos 22 pp 1250105-1– (2012)
[29] DOI: 10.1007/s10827-010-0274-z · doi:10.1007/s10827-010-0274-z
[30] DOI: 10.1142/S0218127408020914 · Zbl 1147.34334 · doi:10.1142/S0218127408020914
[31] DOI: 10.1007/s11571-012-9222-0 · doi:10.1007/s11571-012-9222-0
[32] DOI: 10.1142/S0218127410028112 · Zbl 1208.34114 · doi:10.1142/S0218127410028112
[33] DOI: 10.1142/S0218127412501155 · Zbl 1258.92011 · doi:10.1142/S0218127412501155
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.