Bursting induced by excitatory synaptic coupling in nonidentical conditional relaxation oscillators or square-wave bursters
Bursting induced by excitatory synaptic coupling in nonidentical conditional relaxation oscillators or square-wave bursters
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DOI：
10.1103/physreve.74.021917
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发表时间：
2006-08-01
影响因子：
2.4
通讯作者：
Rubin, Jonathan E.
中科院分区：
文献类型：
--
作者：
Rubin, Jonathan E.
这项工作解释了一种机制，通过这种机制，两个模型细胞之间的兴奋性突触耦合的引入，其中一个是兴奋性的，另一个是紧张性活动时，解耦，导致在所产生的两个细胞网络的爆裂。当单个细胞是条件弛豫振荡器时，这种现象可能会出现，因为它们可以被调谐以参与弛豫振荡，或者当它们是条件方波爆发时。该机制说明了与模型的条件起搏神经元的前Botzinger复杂，以及与此模型的简化形式。在一对一般条件下，证明了在奇异极限下存在周期爆发解。这些条件涉及的持续时间的沉默和活跃阶段的爆裂解决方案的某些结构在相平面中的位置，在适当的突触输入强度。此外，在沉默和活跃阶段的相对流量的附加条件被证明暗示的唯一性和渐近稳定的爆发的解决方案。
This work explains a mechanism through which the introduction of excitatory synaptic coupling between two model cells, one of which is excitable and the other of which is tonically active when uncoupled, leads to bursting in the resulting two-cell network. This phenomenon can arise when the individual cells are conditional relaxation oscillators, in that they can be tuned to engage in relaxation oscillations, or when they are conditional square-wave bursters. The mechanism is illustrated with a model for conditional pacemaker neurons in the pre-Botzinger complex as well as with a reduced form of this model. In the relaxation oscillator case, a periodic bursting solution is proved to exist in the singular limit, under a pair of general conditions. These conditions relate the durations of the silent and active phases of the bursting solution to the locations of certain structures in the phase plane, at appropriate synaptic input strengths. Further, additional conditions on the relative flow rates in the silent and active phases are proved to imply the uniqueness and asymptotic stability of the bursting solution.