Circle maps with gaps: Understanding the dynamics of the two-process model for sleep-wake regulation
Circle maps with gaps: Understanding the dynamics of the two-process model for sleep-wake regulation
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DOI：
10.1017/s0956792518000190
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发表时间：
2018-10-01
影响因子：
1.9
通讯作者：
Skeldon, A. C.
中科院分区：
文献类型：
--
作者：
Bailey, M. P.;Derks, G.;Skeldon, A. C.
30多年来，“双过程模型”在理解睡眠/觉醒调节方面发挥了核心作用。这个表面上简单的模型是非光滑动力系统的一个有趣的例子，其丰富的动力学结构相对未被探索。两个过程模型可以被框定为一个一维地图的圆，其中，对于某些参数制度，有差距。我们展示了如何边界碰撞分岔自然产生的地图与差距扩展和补充阿诺德舌鞍结分岔集，这是一个功能的连续圆地图。新的图片，结果显示如何创建的周期性的解决方案，由鞍结分岔连续地图过渡到周期添加分岔所创建的周期性的解决方案，如在地图间隙。
For more than 30 years the 'two-process model' has played a central role in the understanding of sleep/wake regulation. This ostensibly simple model is an interesting example of a nonsmooth dynamical system, whose rich dynamical structure has been relatively unexplored. The two-process model can be framed as a one-dimensional map of the circle, which, for some parameter regimes, has gaps. We show how border collision bifurcations that arise naturally in maps with gaps extend and supplement the Arnold tongue saddle-node bifurcation set that is a feature of continuous circle maps. The novel picture that results shows how the periodic solutions that are created by saddle-node bifurcations in continuous maps transition to periodic solutions created by period-adding bifurcations as seen in maps with gaps.