Analysis of Interacting Local Oscillation Mechanisms in Three-Timescale Systems
Analysis of Interacting Local Oscillation Mechanisms in Three-Timescale Systems
复制标题
三时标系统中相互作用的局域振荡机制分析
DOI：
10.1137/16m1088429
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Theodore Vo
中科院分区：
文献类型：
--
作者：
Benjamin Letson;J. Rubin;Theodore Vo
慢/快系统中的振荡可以在相空间局部产生，要么是通过快速子系统Hopf分岔的轨迹缓慢通过，要么是由于折叠节点奇点而通过扭曲慢流形的解隧穿。在双时间尺度环境下，快速子系统Hopf和折叠奇点仍然是独立的实体。然而，在三时间尺度的情况下，这些奇点可以相互作用，这允许时间尺度和复杂振荡动力学的有趣混合。使问题进一步复杂化的是，这些三时间尺度问题中的折叠奇点总是接近折叠鞍节点区域，在那里鸭理论失效。在这项工作中，我们研究了三时间尺度系统中的自然情景，其中快速子系统Hopf和折叠节点共存并相互作用，例如在垂体乳营养细胞的电爆发活动和下丘脑神经元分泌促性腺激素释放激素的模型中可以看到。我们分析…
Oscillations in slow/fast systems can be generated locally in phase space from either slow passage of trajectories through fast subsystem Hopf bifurcations, or from solutions tunnelling through twisted slow manifolds due to folded node singularities. In the two-timescale context, the fast subsystem Hopf and folded singularity remain as separate entities. In the three-timescale context, however, these singularities can interact, which allows for an interesting mixing of timescales and complex oscillatory dynamics. To further compound the problem, the folded singularity in these three-timescale problems is always close to the folded saddle-node regime, where canard theory breaks down. In this work, we examine a natural scenario in three-timescale systems where the fast subsystem Hopf and a folded node coexist and interact, as seen for instance in models for the electrical bursting activity in pituitary lactotrophs and for the secretion of gonadotropin releasing hormone by hypothalamic neurons. We analyze a ...
影响因子：
3.5
作者：
BERTRAM, R;BUTTE, MJ;SHERMAN, A
通讯作者：
SHERMAN, A
影响因子：
2.9
作者：
Teka, Wondimu;Tabak, Joel;Bertram, Richard
通讯作者：
Bertram, Richard