Pickard W F
J Math Biol. 1984;21(1):11-23. doi: 10.1007/BF00275219.
The problem of obtaining Helmholtz equivalents for nonlinear resistive one-ports is considered. Two fundamentally different classes of equivalent are described, one local and the other global. For each, necessary and sufficient conditions are derived for the existence and uniqueness of either the Thévenin equivalent or the Norton equivalent or both. These concepts are illustrated (i) by proving that a cell whose channels and pumps are monotone in the membrane potential will, in the absence of net state changes in these ionophores, possess a unique stable resting potential and (ii) by demonstrating that it is in principle impossible to assign unique equivalent circuits to such ionophores.
本文考虑了为非线性电阻单端口获取亥姆霍兹等效电路的问题。描述了两类根本不同的等效电路，一类是局部的，另一类是全局的。对于每一类，推导了戴维南等效电路或诺顿等效电路或两者同时存在且唯一的充要条件。通过以下方式对这些概念进行了说明：(i) 证明一个其通道和泵在膜电位上呈单调变化的细胞，在这些离子载体没有净状态变化的情况下，将具有唯一的稳定静息电位；(ii) 证明原则上不可能为这类离子载体赋予唯一的等效电路。
