Presentation 2004-07-16 Tracing Solution Curves and Bifurcation Points Using SPICE Seizo HAGINO, Yoshifumi NISHIO, Akio USHIDA, PDF download Page Link (See Japanese page) It is very important to calculate the multiple solutions of nonlinear equations, because there are many kind of resistive circuits such as flip-flops and Schmitt-trigger which have the multiple DC solutions. Although interval methods [2]-[3] can find all the solutions, it is rather time-consuming for large scale systems. The homotopy methods [4]-[6] are also applied to calculate the multiple solutions of nonlinear equations. There have been proposed many efficient algorithms using SPICE simulators [5]-[6] whose algorithms are based on the homotopy methods. Although they can efficiently find the multiple solutions, it is not known whether they have gotten all the solutions or not. The homotopy paths may consist of the multiple independent branches and the closed loops, whose branches may cross at the points called pitchfork bifurcation points. Unfortunately, the curve tracing algorithm based on arc-length method [6] may fail to trace the curve, because the rank of the n×(n+1) Jacobian matrix of nonliner equation is reduced to equal or less than n-1 at the points. In this paper, we propose an efficient SPICE-oriented algorithm for finding the limit points and/or bifurction points. We aslo show the directions of sotution curves stating the sigular points. (See Japanese page) tracing solution curve / limit point / bifurcation points / nonlinear algebraic equation / SPICE NLP2004-27

Committee Conference Information NLP 2004/7/9(1days) (See Japanese page) (See Japanese page)

Registration To Paper Information Nonlinear Problems (NLP) JPN (See Japanese page) (See Japanese page) Tracing Solution Curves and Bifurcation Points Using SPICE tracing solution curve limit point bifurcation points nonlinear algebraic equation SPICE Seizo HAGINO Dept. of Electrical and Electronic Engineering, Tokushima University() Yoshifumi NISHIO Dept. of Electrical and Electronic Engineering, Tokushima University Akio USHIDA Dept. of Electrical and Electronic Engineering, Tokushima University 2004-07-16 NLP2004-27 vol.104 197 pp.pp.- 6