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:R2 x RN →R RN. A combination of methods in [5] and [7] requires finding zeros of an extended system of 4_N+3 variables. Shintani and Kanda [6] proposes another algorithm, in which computation of extended system of 3_N+3 variables is sufficient. On the contrary, in our algorithm, we should find zeros of another extended system of 3_N_+2 variables.