Bifurcation mechanism for emergence of spontaneous oscillations in coupled heterogeneous excitable units
Bifurcation mechanism for emergence of spontaneous oscillations in coupled heterogeneous excitable units
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DOI：
10.1103/physreve.98.052210
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发表时间：
2018-11
影响因子：
2.4
通讯作者：
K. Morino;G. Tanaka;K. Aihara
中科院分区：
文献类型：
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作者：
K. Morino;G. Tanaka;K. Aihara
生物系统通常由各种不同的可兴奋单位组成。研究这种异质性如何影响生物系统的集体行为是一个有趣的问题。为了了解单位异质性对集体振荡行为开始的动力学机制的影响，我们分析了耦合的异质可激发单位。我们阐明了自发振荡是如何根据单位的异质性程度而出现的。随着耦合强度的增加，系统经历了鞍结点不变圆分叉和异宿分叉。基于分叉理论，我们揭示了这两个分叉的顺序在自发振荡产生的机制中起着关键作用。此外，我们还分析表明，当系统具有对称性时，会出现五阶的干草分叉，而不是两个分叉。我们还发现，当不同参数的可激发单元子群体的大小比较平衡时，更容易发生自发振荡。
Biological systems are often composed of various heterogeneous excitable units. It is a fascinating problem to investigate how this heterogeneity affects collective behavior of biological systems. In this paper, to understand the effect of the unit heterogeneity on the dynamical mechanism for the onset of collective oscillatory behavior, we analyze coupled heterogeneous excitable units. We clarify how spontaneous oscillations emerge depending on the degree of heterogeneity of the units. With an increase in the coupling strength, the system undergoes a saddle-node on invariant circle bifurcation and a heteroclinic bifurcation. Based on bifurcation theory, we reveal that the order of the two bifurcations plays key roles in the mechanism of the emergence of spontaneous oscillations. In addition, we analytically show that when the system has a symmetric property, a 5th-order pitchfork bifurcation occurs instead of the two bifurcations. We also find that spontaneous oscillations are more likely to occur when the sizes of subpopulations of excitable units with different parameters are more balanced.