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A series of bifurcation scenarios in the firing pattern transitions in an experimental neural pacemaker. (English) Zbl 1064.37071

Summary: Various bifurcation scenarios from period-1 bursting to period-1 spiking via a complex procedure were simulated in previous theoretical studies on neuronal models. The results revealed a general principle of neuronal firing pattern transitions. In this letter, three types of bifurcation scenarios with respect to extracellar calcium concentration (\([\text{Ca}^{++}]_o\)) were discovered in experiments on neural pacemakers. Such a series of bifurcation scenarios implied complex structure of bifurcations in the firing pattern transitions of neurons. In the two-dimensional parameter space of Chay model, three classical kinds of bifurcation scenarios with respect to the bifurcation parameter \(v_c\) (the reverse potential of calcium concentration) were simulated. By the variation of the conditional parameter, \(\lambda_n\), the relationship among the three bifurcation scenarios was revealed. The results not only verified the existence of different bifurcation scenarios in real neuronal system, but also indicated that the differences among the bifurcation scenarios were caused by the different configuration of parameters. The physiological significance of such bifurcation

MSC:

37N25 Dynamical systems in biology
92C99 Physiological, cellular and medical topics
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[1] DOI: 10.1016/0304-3959(88)90209-6
[2] DOI: 10.1016/0167-2789(85)90060-0 · Zbl 0582.92007
[3] DOI: 10.1142/S0218127495000491 · Zbl 0885.92019
[4] DOI: 10.1016/S0006-3495(98)77504-6
[5] DOI: 10.1016/0960-0779(93)90029-Z · Zbl 0777.92003
[6] DOI: 10.1016/0960-0779(93)90047-5 · Zbl 0855.34051
[7] DOI: 10.1007/BF00198918 · Zbl 0805.92005
[8] DOI: 10.1016/0167-2789(83)90126-4 · Zbl 0561.58029
[9] Gong Y. F., Biol. Cybern. 78 pp 159–
[10] DOI: 10.1097/00001756-200209160-00018
[11] DOI: 10.1016/S0375-9601(01)00278-X · Zbl 01616595
[12] DOI: 10.1016/0960-0779(92)90032-I · Zbl 0766.92006
[13] DOI: 10.1016/0960-0779(92)90012-C · Zbl 0753.92009
[14] DOI: 10.1016/0960-0779(92)90055-R · Zbl 0766.92007
[15] DOI: 10.1142/S0218127497001448
[16] DOI: 10.1097/00001756-200107200-00016
[17] DOI: 10.1097/00001756-200312020-00004
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