耦合椭圆脉冲串的脉冲串内同步变化
Within-burst synchrony changes for coupled elliptic bursters
摘要：
我们研究了一种新的现象的外观线性耦合相同的突发：同步突发，其中有变化的尖峰同步内的每个突发。我们研究的例子是正常形式的椭圆爆发，有一个周期性的缓慢通过Bautin（余维两个退化Andronov-Hopf）分歧。该爆发器在重复尖峰的开始处具有亚临界Andronov-Hopf分叉，而爆发的结束通过折叠极限环分叉发生。研究了线性直接耦合下两个和三个Bautin型椭圆脉冲串的同步行为。已知突发同步是这种耦合突发之间的普遍行为，而尖峰同步更依赖于耦合的细节。我们注意到，高阶项在正常的形式，不影响一个单一的突发的行为可以负责同步模式的变化，更准确地说，我们发现内突发同步变化与尖峰频率的转折点。
英文摘要：
We study the appearance of a novel phenomenon for linearly coupled identical bursters: synchronized bursts where there are changes of spike synchrony within each burst. The examples we study are for normal form elliptic bursters where there is a periodic slow passage through a Bautin (codimension two degenerate Andronov-Hopf) bifurcation. This burster has a subcritical Andronov-Hopf bifurcation at the onset of repetitive spiking while end of burst occurs via a fold limit cycle bifurcation. We study synchronization behavior of two and three Bautin-type elliptic bursters for a linear direct coupling scheme. Burst synchronization is known to be prevalent behavior among such coupled bursters, while spike synchronization is more dependent on the details of the coupling. We note that higher order terms in the normal form that do not affect the behavior of a single burster can be responsible for changes in synchrony pattern; more precisely, we find within-burst synchrony changes associated with a turning point in the spiking frequency.
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