Bifurcation Analysis of Nonlinear Resistive Circuits by Curve Tracing Method

概要

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In this paper, we discuss computational methods for obtaining the bifurcation points and the branch directions at branching points of solution curves for the nonlinear resistive circuits. There are many kinds of the bifurcation points such as limit point, branch point and isolated point. At these points, the Jacobian matrix of circuit equation becomes singular so that we cannot directlyapply the usual numerical techniques such as Newton-Raphson method. Therefore, we propose a simple modification technique such that the Newton-Raphson method can be also applied to the modified equations. On the other hand, a curve tracing algorithm can continuously trace the solution curves having the limit points and/or branching points. In this case, we can see whether the curve has passed through a bifurcation point or not by checking the sign of determinant of the Jacobian matrix. We also propose two different methods for calculating the directions of branches at branching point. Combining these algorithms, complicated solution curves will be easily traced by the curve tracing method. We show the example of a Hopfield network in Sect. 5.
社団法人電子情報通信学会の論文
1995-09-25