Bifurcations and Saddle-Sink-Source Networks in Variable-Independent Quadratic Systems

Abstract

This paper presents a theory for nonlinear dynamics of dynamical systems possessing variable-independent univariate quadratic vector fields. The dynamical systems with a constant vector field and a variable-independent quadratic vector field are presented first, and the 1-dimensional flows discussed. Dynamical systems with linear and quadratic variable-independent univariate vector fields are discussed, and the corresponding bifurcation and global dynamics are discussed. Dynamical systems with two variable-independent univariate quadratic vector fields are analyzed, and the corresponding bifurcations and global dynamics are discussed through the first integral manifolds.