Self-similar solution of distributed linear and nonlinear networks

作者：Karl E. Lonngren, H. Hsuan, N.R. Malik, Hanbin Shen · 发表于：IEEE Transactions on Circuits and Systems · 年份：1975 · DOI：10.1109/tcs.1975.1083992 · 被引用次数：9 · 研究领域：Nonlinear Dynamics and Pattern Formation、Neural Networks Stability and Synchronization、Matrix Theory and Algorithms

The method of "self-similar solution of partial differential equations" is introduced and applied to the distributed RGC network. For linear networks convolution integrals,V(x,t) = V_{\delta} \times V_{source}andV(x,t) = V_{\delta'} \times I_{source}are obtained whereV_\deltaandV_\delta'are, respectively, the responses to the\deltafunction voltage and current sources found and from the self-similar analysis, andV_sourceandI_{source} \propto \partial V_{source}/\partial xare arbitrary voltage and current sources. For certain sources, these integrals have been performed and the results will be presented. The technique is also successfully applied to nonlinear networks which are useful in modeling various microelectronic circuit components.