The dynamics of quantifiable homeostasis. II. Characterization of linear processes.
The dynamics of quantifiable homeostasis. II. Characterization of linear processes.
复制标题
可量化的动态平衡。
DOI：
10.1002/ajmg.1320150415
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发表时间：
1983
期刊：
影响因子：
--
通讯作者：
Edmond A. Murphy
中科院分区：
文献类型：
--
作者：
W. A. Renie;Edmond A. Murphy
本文论述了生理稳态过程的数学模型，导致滞后微分方程的代表性。它专门处理线性反馈过程。据推测，在许多系统中，在对来自平衡的标准扰动的响应中，恢复力起作用的强度（用常数B表示）是一种遗传特征，而平均值或归巢值可能是，也可能不是。求解了具有线性反馈的一类方程。该解决方案提供了预测，实验数据可以进行测试。三种类型的位移从归巢值被确认：漂移，灾难，和扫视。介绍了几种数学函数的求值方法。它们是前向递归，后向递归，数值积分，稳态解，和反转的亥维赛展开的拉普拉斯变换。稳态过程的条件，导致阻尼非振荡响应，阻尼振荡响应，稳定的振荡，和不受控制的振荡。讨论了相关惩罚的概念，该惩罚取决于自导引值的位移程度。惩罚是通过线性、二次和三次成本的数值积分来评估的。多项式函数的成本可以通过线性加权来找到。最佳响应强度（即产生最小成本的响应强度）是针对这些成本函数中的每一个计算的。
This paper deals with the representation of physiological homeostatic processes by mathematical models that lead to lag-differential equations. It deals exclusively with feedback processes that are linear. It is surmised that in the response to standard perturbations from equilibrium, in many systems the strength at which the restorative force works (denoted by the constant b) is a genetic characteristic, while the average or homing value may or may not be. The class of equations with linear feedback is solved. The solution provides predictions against which experimental data may be tested. Three types of displacement from the homing value are recognized: drifts, catastrophes, and saccades. Several methods of evaluating the mathematical functions are described. They are forward recursion, backward recursion, numerical integration, steady-state solutions, and inversion of the Heaviside expansion of the Laplace transform. Conditions for homeostatic processes that result in damped nonoscillating responses, damped oscillating responses, stable oscillations, and uncontrolled oscillations are derived. The concept of an associated penalty that depends on the degree of displacement from the homing value is discussed. Penalties are evaluated by numerical integration for linear, quadratic, and cubic costs. Costs for polynomial functions may be found by linear weighting. The optimum strength of response (ie, the one that produces the minimum cost) is calculated for each of these cost functions.