Higher order predictors for the LPC curve near Bautin bifurcation in ODEs and DDEs

Abstract

The Bautin bifurcation is a well-studied codim 2 bifurcation where the system has an equilibrium with a pair of simple purely imaginary eigenvalues and the vanishing first Lyapunov coefficient. Generically, a codim1 bifurcation curve of nonhyperbolic limit cycles (LPC curve) emanates from a Bautin point. In this thesis, we derive higher-order predictors for the LPC curve in ODEs and DDEs for the first time by performing the parameter-dependent center manifold reduction near the Bautin point.