Investigation of Global Bifurcations in Planar Vector Fields

摘要

The general area of the research has been the investigation of nonlinear dynamical systems and their bifurcations . A number of different investigations of bifurcation in multiparameter systems of differential equations have been undertaken. (1) The investigation of global bifurcations in planar vector fields: In studying higher codimension bifurcations in models of chemical reactors, it was necessary to study codimension two bifurcations involving the presence of homoclinic orbits for these systems. A classification of codimension two bifurcations involving a single saddle point was constructed and applied to chemical reactor problems. (2) The investigation of dynamical systems with symmetry groups: A significant discovery is the occurrence of heteroclinic cycles that are structurally stable within the class of symmetric systems. (3) The investigation of one dimensional mappings; Attracting Cantor sets that occur at the limit of period doubling sequences of bifurcations have Lebesgue measure zero. (jhd)