### 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 language | English |
---|---|

Pages (from-to) | 11-18 |

Number of pages | 8 |

Journal | Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi) |

Volume | 68 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1985 |

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### ASJC Scopus subject areas

- Computer Networks and Communications
- Electrical and Electronic Engineering

### Cite this

*Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)*,

*68*(6), 11-18. https://doi.org/10.1002/ecja.4410680602

**A constructive approach to the analysis of nonlinear resistive circuits based on the fixed point algorithm theory.** / Member, Yuzo Sumi, Regular; Oishi, Shinichi; Takase, Tadaaki; Members, Kazuo Horiuchi, Regular.

Research output: Contribution to journal › Article

*Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)*, vol. 68, no. 6, pp. 11-18. https://doi.org/10.1002/ecja.4410680602

}

TY - JOUR

T1 - A constructive approach to the analysis of nonlinear resistive circuits based on the fixed point algorithm theory

AU - Member, Yuzo Sumi, Regular

AU - Oishi, Shinichi

AU - Takase, Tadaaki

AU - Members, Kazuo Horiuchi, Regular

PY - 1985

Y1 - 1985

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84984281946&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84984281946&partnerID=8YFLogxK

U2 - 10.1002/ecja.4410680602

DO - 10.1002/ecja.4410680602

M3 - Article

AN - SCOPUS:84984281946

VL - 68

SP - 11

EP - 18

JO - Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)

SN - 8756-6621

IS - 6

ER -