Parallel Computing of 2-D Bifurcation Diagrams in Circuits With Electric Arcs

Abstract

It is shown that a relatively simple dynamical dc electric arc model shows complicated two-parameter (2-D) bifurcations with both periodic and chaotic responses. 2-D bifurcation diagrams for the arc model [a system of three ordinary differential equations (ODEs)] are obtained by using parallel computations because obtaining a single 2-D diagram requires solving the ODE system hundreds of thousands or even a few millions of times (depending on the intervals of parameters and assumed resolution). Several color 2-D bifurcation diagrams are presented, and the speedup factors of their parallel computations are provided. Numerical computations of periodic and chaotic responses of the 2-D bifurcation diagrams are confirmed by both the one-parameter (1-D) diagrams and the 0-1 test for chaos. Some further theoretical aspects of parallel computing of 2-D bifurcation diagrams are also considered.