Angular homeostasis. IX. Polygonal orbits with a moving target: implications for anomalous numbers of digits in congenital heart disease.
Angular homeostasis. IX. Polygonal orbits with a moving target: implications for anomalous numbers of digits in congenital heart disease.
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角稳态。
DOI：
10.1002/ajmg.1320450321
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
Murphy,EA
中科院分区：
文献类型：
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作者：
Murphy,EA
本文探讨了离散过程的性质，在这个过程中，追踪者寻找一个以恒定速度运动的目标，这个速度是追踪者速度的一个固定比例。追踪者受到比例角稳态的影响，因此选择每个回路的步数很小。相对于目标的轨道可以采取以下四种形式中的任何一种：将它们的方向反转无限次的多边形;或者在有限次反转之后最终具有整数条边的多边形;或者具有有理数条边的多边形;或者具有密集填充环形的无理数条边的多边形。没有一个多边形是规则的。在参数空间中，第一个集合和其他三个集合之间的边界线有一个有点奇怪的图案，可能是分形的，但没有证据。与固定目标的图案不同，可能有一组或一系列不同的速比r值和修正系数b值，所有这些值都导致具有特定边数n的图形（尽管顶点在不同位置）。仅为缠绕数为1的多边形找到汇流。的影响进行了讨论，这个属性的生物性状的遗传编码是可数的。当校正系数是周期性弧或时间依赖的时，一些注意力也被支付到多边形与个体发育生长的相关性。© 1993 Wiley‐利斯公司
This paper explores properties of discrete processes in which a pursuer seeks a target that is moving at constant velocityrthat is a fixed proportion of the speed of the pursuer. The pursuer is subjected to proportional angular homeostasis, so chosen that the number of steps per circuit is small. The orbits relative to the target may assume any of four forms: polygons that reverse their sense an infinite number of times; or polygons that after a finite number of reversals ultimately come to have an integer numbers of sides; or have a rational numbers of sides; or have an irrational number of sides that densely fill an annulus. None of the polygons is regular. In the parameter space, the boundary line between the first of these sets and the other three has a somewhat bizarre pattern and may possibly be fractal, but no proof is forthcoming. Unlike the pattern with a stationary target, there may be a set orcatchmentof diverse values of the speed ratio,r, and the correction coefficient,bthat all result in figures of some specified number,n, of sides (although with vertices in differing locations). Catchments have been found for only those polygons that have the winding number of 1. The implications are discussed that this property has for the genetic coding of biological traits that are countable. Some attention is also paid to the relevance of polygons with few sides to ontogenic growth when the correction coefficient is cyclically arc‐ or time‐dependent. © 1993 Wiley‐Liss, Inc.