COMPUTATION OF SINGULARITIES IN LARGE NONLINEAR SYSTEMS

摘要

A general approach is proposed for the numerical computation of one-parameter singularities in the sense of Golubitsky and Schaeffer [Singularities and Groups in Bifurcation Theory, Vol. I, Springer-Verlag, Berlin, 1985]. The singularities of codimension three or less are organized in a new way. Our scheme is close to the numerics and in some cases gives explicit expressions for the defining equations (obtained inductively) where no such expressions were previously available. The numerical computation by the Lyapunov-Schmidt reduction summarizes work by many authors during the last 20 years, treating all cases in a unified way. A numerical example is provided where singularities with codimension up to three are detected and computed in a parameterized boundary value problem. [References: 30]