An Algorithm for Computing a Nondegenerate Hysteresis Point

Abstract

We propose an algorithm for computing nondegenerate hysteresis points arising in bifurcation problems with two parameters such as $G:{\mathbf{R}}^2\times {\mathbf{R}}^N\to {\mathbf{R}}^N$. A combination of methods in [5] and [7] requires finding zeros of an extended system of $4N+3$ variables. Shintani and Kanda [6] proposes another algorithm, in which computation of extended system of $3N+3$ variables is sufficient. On the contrary, in our algorithm, we should find zeros of another extended system of $3N+2$ variables.