The simplest normal form and its application to bifurcation control (Q2468193)

Normal form theory is one of the useful tools in the study of nonlinear dynamical systems. The main idea is to apply successive coordinate transformations in order to get a form of the original system as a simple as possible. The new form is qualitatively equivalent to the original system and thus the dynamical analysis is greatly simplified. A conventional normal form is in general not unique and can be further simplified using similar near-identity transformations, leading to the simplest normal form. This paper is concerned with the computation of the simplest normal forms with perturbation parameters associated with codimension-one singularities, and applications to control systems. It is shown that, unlike the classical normal forms, the simplest normal forms for single zero and Hopf singlarities are finite up to an arbitrary order. Symbolic programs have been developed using Maple.