On the application of degree theory to the analysis of resistive nonlinear networks
On the application of degree theory to the analysis of resistive nonlinear networks
复制标题
度理论在阻性非线性网络分析中的应用
DOI：
10.1002/cta.4490050106
复制
发表时间：
1977
影响因子：
2.3
通讯作者：
Niantsu N. Wang
中科院分区：
文献类型：
--
作者：
L. Chua;Niantsu N. Wang
本文将映射的度理论应用于电阻性非线性网络解的存在性及相关问题的研究。在这方面的许多著名的结果已被推广到允许非线性电阻之间的耦合。要求非线性电阻最终增加的通常假设已经通过仅要求电阻最终是无源的而被大大削弱。而不是调查特殊情况下的特殊技术，我们研究的网络方程从几何的角度来看。奇域同伦的概念为分析一大类实际的非线性网络提供了一种统一而简单的方法。许多已知的结果属于这一类，并作为我们的推广定理的特例导出。这种方法导致更好地理解与网络方程相关联的向量场的几何结构。结果，就解的存在性而言，最终被动性的概念比最终递增性的概念更基本。最终无源性概念的强调也自然导致非线性电阻之间的耦合。
奇域的同伦也为寻找解提供了一些有用的技巧。沿着这条线，我们还研究了边界区域的解决方案，并讨论了非线性电阻的工作范围。
This paper presents an application of the theory of the degree of a map to the study of the existence of solutions and some related problems for resistive nonlinear networks. Many well-known results in this area have been generalized to allow coupling among the nonlinear resistors. The usual hypothesis requiring the nonlinear resistors to be eventually increasing has been weakened considerably by only requiring the resistors to be eventually passive. Instead of investigating special cases by special techniques, we study the network equations from a geometrical point of view. The concept of homotopy of odd fields provides a unified yet simple approach for analyzing a large class of practical nonlinear networks. Many known results belong to this category and are derived as special cases of our generalized theorems. This approach leads to a much better understanding of the geometric structure of the vector fields associated with the network equations. As a result, in so far as the existence of solutions is concerned, the concept of eventual passivity is shown to be far more basic than that of eventual increasingness. The emphasis of the concept of eventual passivity also leads naturally to the inclusion of coupling among the nonlinear resistors.
The homotopy of odd fields also provides some useful techniques for locating the solutions. Along this line, we also study the bounding region of solutions and discuss the operating range of nonlinear resistors.