  An elliptic Newton flow is a dynamical system that can be interpreted as a
continuous version of Newton's iteration method for finding the zeros of an
elliptic function f. Previous work focusses on structurally stable flows (i.e.,
the phase portraits are topologically invariant under perturbations of the
poles and zeros for f), including a classification / representation result for
such flows in terms of Newton graphs (i.e., cellularly embedded toroidal graphs
fulfilling certain combinatorial properties). The present paper deals with
non-structurally stable elliptic Newton flows determined by pseudo Newton
graphs (i.e., cellularly embedded toroidal graphs, either generated by a Newton
graph, or the so called nuclear Newton graph, exhibiting only one vertex and
two edges). Our study results into a deeper insight in the creation of
structurally stable Newton flows and the bifurcation of non-structurally stable
Newton flows.
