A constructive approach to the analysis of nonlinear resistive circuits based on the fixed point algorithm theory

Yuzo Sumi, Regular Member, Shinichi Oishi, Tadaaki Takase, Kazuo Horiuchi, Regular Members

    Research output: Contribution to journalArticle

    Abstract

    The existence problem for solution of a nonlinear resistive circuit and the problem of identifying the number of the solutions are classic and basic problems in circuit theory. In their paper “On the application of degree theory to the analysis of resistive nonlinear networks” (Int. J. Cir. Theor. Appl., 5, pp. (1977)), Chua and Wang presented a unified theory for the existence of solutions for nonlinear circuit equations. That is, on the basis of the degree theory the existence of solutions of many nonlinear resistive circuits can be guaranteed in a unified manner by showing that the circuit equations are homotopic to certain odd fields. Their arguments are, however, not constructive. In this paper, an algorithm based on the fixed‐point algorithm theory is presented and it is proved that by this algorithm at least one solution can always be constructed for nonlinear circuit equations whose solutions are guaranteed to exist by Chua and Wang's theorems. Usefulness of the algorithm is also demonstrated by a few examples.

    Original languageEnglish
    Pages (from-to)11-18
    Number of pages8
    JournalElectronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)
    Volume68
    Issue number6
    DOIs
    Publication statusPublished - 1985

    ASJC Scopus subject areas

    • Computer Networks and Communications
    • Electrical and Electronic Engineering

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