Synchronization of oscillators via active media
Synchronization of oscillators via active media
复制标题
通过有源介质同步振荡器
DOI：
10.1103/physreve.99.052218
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发表时间：
2019
影响因子：
2.4
通讯作者：
Ermentrout, Bard
中科院分区：
文献类型：
--
作者：
Orr, Derek;Ermentrout, Bard
在这篇文章中，我们研究通过有源(可激发)细胞间接耦合的振子对。我们介绍了耦合振子和可激发细胞的标量相模型。我们首先证明了一个可激发晶胞和一个振荡晶胞将在不同的模式下显示出锁相。接下来，我们引入第二个振荡池，并证明唯一的吸引子是振荡器之间的同步。我们还将研究可兴奋细胞激发或静止时对异质性的稳健性。接下来，我们研究振荡器通过两个可激发单元耦合时的动力学。在这种情况下，动力学是非常复杂的，具有多种形式的双稳态，在某些情况下，还具有混沌行为。我们还将弱耦合分析应用于这种情况，并解释了分岔图中观察到的一些简并现象。此外，我们观察了通过可兴奋细胞的长链耦合的振荡器对，并表明振荡器频率的微小差异使它们的锁定更加稳健。最后，我们演示了在Morris-LeCar神经元缝隙-结耦合系统的相位模型中看到的许多相同的现象。
In this paper, we study pairs of oscillators that are indirectly coupled via active (excitable) cells. We introduce a scalar phase model for coupled oscillators and excitable cells. We first show that one excitable and one oscillatory cell will exhibit phase locking at a variety ofpatterns. We next introduce a second oscillatory cell and show that the only attractor is synchrony between the oscillators. We will also study the robustness to heterogeneity when the excitable cell fires or is quiescent. We next examine the dynamics when the oscillators are coupled via two excitable cells. In this case, the dynamics are very complicated with many forms of bistability and, in some cases, chaotic behavior. We also apply weak-coupling analysis to this case and explain some of the degeneracies observed in the bifurcation diagram. Further, we look at pairs of oscillators coupled via long chains of excitable cells and show that small differences in the frequency of the oscillators makes their locking more robust. Finally, we demonstrate many of the same phenomena seen in the phase model for a gap-junction coupled system of Morris-Lecar neurons.